relation between coefficients and roots of quadratic polynomial?

Question

What is the relation between roots of a quadratic polynomial and the coefficients of the x^2,x and constant terms?

Answer 1

consider the polynomial aX^2+bX+c . let the roots be X1 and X2. then the following relations hold true for all X1 and X2.

X1+X2 = - (b/a) X1*X2 = (c/a).

Answer 2

Sum of the roots = -(x coefficient)/x^2 coefficient)

Product of roots = Constant term/x^2 coefficient

Answer 3

shree dharacharya great mathematician of india gives relation between roots of quadratic eq. but there is no relation define for quadratic polynomial.

Answer 4

The equation has distinct integer roots, so m=(p^2-4q)^1/2 is a integer number. It implies (p-m)(p+m)=4q. It is trial to check that p-m and p+m are both even number. We have 4 cases (note that q is a prime): From three cases : 1)p-m=2. 2)p-m=4. 3)p-m=2q. we can see that q=2 and p=3 the fourth case (p-m=4q) is false. (proof from Vietnam)

Answer 5

sum of the roots = - (coefficient of x) / (coefficient of x^2)

product of the roots = (constant term) / (coefficient of x^2)

Answer 6

The polynomial is
a(x - x1)(x - x2) = a(x^2 -x*x1 - x*x2 + x1*x2) =
= a[x^2 - (x1 + x2)x + x1*x2) = ax^2 - (x1 + x2)ax + x1*x2*a

Answer 7

Coefficients
1. A number or symbol multiplied with a variable or an unknown quantity in an algebraic term, as 4 in the term 4x, or x in the term x(a + b).
2. A numerical measure of a physical or chemical property that is constant for a system under specified conditions such as the coefficient of friction.

1. A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. For example, 4 is the coefficient in the term 4x, and x is the coefficient in x(a + b).
2. A numerical measure of a physical or chemical property that is constant for a system under specified conditions. The speed of light in a vacuum, for example, is a constant.

Root
a part of the body of a plant that develops, typically, from the radicle and grows downward into the soil, anchoring the plant and absorbing nutriment and moisture.
2. a similar organ developed from some other part of a plant, as one of those by which ivy clings to its support.
3. any underground part of a plant, as a rhizome.
4. something resembling or suggesting the root of a plant in position or function: roots of wires and cables.
5. the embedded or basal portion of a hair, tooth, nail, nerve, etc.
6. the fundamental or essential part: the root of a matter.
7. the source or origin of a thing: The love of money is the root of all evil.
8. a person or family as the source of offspring or descendants.
9. an offshoot or scion.
10. Mathematics.
a. a quantity that, when multiplied by itself a certain number of times, produces a given quantity: The number 2 is the square root of 4, the cube root of 8, and the fourth root of 16.
b. rth root, the quantity raised to the power 1/r: The number 2 is the 1/3 root of 8.
c. a value of the argument of a function for which the function takes the value zero.
11. Grammar.
a. a morpheme that underlies an inflectional or derivational paradigm, as dance, the root in danced, dancer, or ten-, the root of Latin tendere “to stretch.”
b. such a form reconstructed for a parent language, as *sed-, the hypothetical proto-Indo-European root meaning “sit.”
12. roots,
a. a person's original or true home, environment, and culture: He's lived in New York for twenty years, but his roots are in France.
b. the personal relationships, affinity for a locale, habits, and the like, that make a country, region, city, or town one's true home: He lived in Tulsa for a few years, but never established any roots there.
c. personal identification with a culture, religion, etc., seen as promoting the development of the character or the stability of society as a whole.
13. Music.
a. the fundamental tone of a compound tone or of a series of harmonies.
b. the lowest tone of a chord when arranged as a series of thirds; the fundamental.
14. Machinery.
a. (in a screw or other threaded object) the narrow inner surface between threads. Compare crest (def. 18), flank (def. 7).
b. (in a gear) the narrow inner surface between teeth.
15. Australian Informal. an act of sexual intercourse.
16. Shipbuilding. the inner angle of an angle iron.
–verb (used without object)
17. to become fixed or established.
–verb (used with object)
18. to fix by or as if by roots: We were rooted to the spot by surprise.
19. to implant or establish deeply: Good manners were rooted in him like a second nature.
20. to pull, tear, or dig up by the roots (often fol. by up or out).
21. to extirpate; exterminate; remove completely (often fol. by up or out): to root out crime.
—Idioms
22. root and branch, utterly; entirely: to destroy something root and branch.
23. take root,
a. to send out roots; begin to grow.
b. to become fixed or established: The prejudices of parents usually take root in their children.
1. The usually underground portion of a plant that lacks buds, leaves, or nodes and serves as support, draws minerals and water from the surrounding soil, and sometimes stores food.
2. Any of various other underground plant parts, especially an underground stem such as a rhizome, corm, or tuber.
3.
1. The embedded part of an organ or structure such as a hair, tooth, or nerve, that serves as a base or support.
2. A base or support: We snipped the wires at the roots.
3. The condition of being settled and of belonging to a particular place or society. Often used in the plural: Our roots in this town go back a long way.
4. roots The state of having or establishing an indigenous relationship with or a personal affinity for a particular culture, society, or environment: music with unmistakable African roots.
5. The element that carries the main component of meaning in a word and provides the basis from which a word is derived by adding affixes or inflectional endings or by phonetic change.
6. Such an element reconstructed for a protolanguage. Also called radical.
7. A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, a fourth root of 4 is √2. Also called nth root.
8. A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
9. A number at which a polynomial has the value zero.
10. The note from which a chord is built.
11. Such a note occurring as the lowest note of a triad or other chord.
4. An essential part or element; the basic core: I finally got to the root of the problem.
5. A primary source; an origin. See Synonyms at origin.
6. A progenitor or ancestor from which a person or family is descended.
7.
1. The condition of being settled and of belonging to a particular place or society. Often used in the plural: Our roots in this town go back a long way.
2. roots The state of having or establishing an indigenous relationship with or a personal affinity for a particular culture, society, or environment: music with unmistakable African roots.
3. The element that carries the main component of meaning in a word and provides the basis from which a word is derived by adding affixes or inflectional endings or by phonetic change.
4. Such an element reconstructed for a protolanguage. Also called radical.
5. A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, a fourth root of 4 is √2. Also called nth root.
6. A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
7. A number at which a polynomial has the value zero.
8. The note from which a chord is built.
9. Such a note occurring as the lowest note of a triad or other chord.
8. Linguistics
1. The element that carries the main component of meaning in a word and provides the basis from which a word is derived by adding affixes or inflectional endings or by phonetic change.
2. Such an element reconstructed for a protolanguage. Also called radical.
3. A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, a fourth root of 4 is √2. Also called nth root.
4. A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
5. A number at which a polynomial has the value zero.
6. The note from which a chord is built.
7. Such a note occurring as the lowest note of a triad or other chord.
9. Mathematics
1. A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, a fourth root of 4 is √2. Also called nth root.
2. A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
3. A number at which a polynomial has the value zero.
4. The note from which a chord is built.
5. Such a note occurring as the lowest note of a triad or other chord.
10. Music
1. The note from which a chord is built.
2. Such a note occurring as the lowest note of a triad or other chord.
1. To grow roots or a root.
2. To become firmly established, settled, or entrenched.
3. To come into existence; originate.

1. To cause to put out roots and grow.
2. To implant by or as if by the roots.
3. To furnish a primary source or origin to.
4. To remove by or as if by the roots. Often used with up or out: "declared that waste and fraud will be vigorously rooted out of Government" (New York Times).

To dig with or as if with the snout or nose: Even a blind hog can root up an acorn.

v. intr.

1. To dig in the earth with or as if with the snout or nose.
2. To rummage for something: rooted around for a pencil in his cluttered office.


1. To give audible encouragement or applause to a contestant or team; cheer. See Synonyms at applaud.
2. To lend support to someone or something.


the condition of belonging to a particular place or group by virtue of social or ethnic or cultural lineage; "his roots in Texas go back a long way"; "he went back to Sweden to search for his roots"; "his music has African roots"
1. A plant part that usually grows underground, secures the plant in place, absorbs minerals and water, and stores food manufactured by leaves and other plant parts. Roots grow in a root system. Eudicots and magnoliids have a central, longer, and larger taproot with many narrower lateral roots branching off, while monocots have a mass of threadlike fibrous roots, which are roughly the same length and remain close to the surface of the soil. In vascular plants, roots usually consist of a central cylinder of vascular tissue, surrounded by the pericycle and endodermis, then a thick layer of cortex, and finally an outer epidermis or (in woody plants) periderm. Only finer roots (known as feeder roots) actively take up water and minerals, generally in the uppermost meter of soil. These roots absorb minerals primarily through small epidermal structures known as root hairs. In certain plants, adventitious roots grow out from the stem above ground as aerial roots or prop roots, bending down into the soil, to facilitate the exchange of gases or increase support. Certain plants (such as the carrot and beet) have fleshy storage roots with abundant parenchyma in their vascular tissues. See also fibrous root, taproot.
2. Any of various other plant parts that grow underground, especially an underground stem such as a corm, rhizome, or tuber.
3. The part of a tooth that is embedded in the jaw and not covered by enamel.
4. Mathematics
1. A number that, when multiplied by itself a given number of times, produces a specified number. For example, since 2 × 2 × 2 × 2 = 16, 2 is a fourth root of 16.
2. A solution to an equation. For example, a root of the equation x2 - 4 = 0 is 2, since 22 - 4 = 0.


(1976) A Pulitzer Prize–winning novel by the African-American author Alex Haley, later made into a popular television drama. It traces a black American man's heritage to Africa, where his ancestors had been captured and sold as slaves.
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