Algebra Question!!?

Question

I have no idea what this means....

5. Using the discriminant, determine the nature of the roots of the following equations (DO NOT SOLVE):

a) x2 + 4x – 1 = 0

b) 2n2 – 3n + 5 = 0


6. Find the roots using the quadratic formula.
a) 3x2 – 2x + 5 = 0

b) 2t2 + 6t – 3 = 0



THANKS EVERYBODY!!!

Answer 1

The discriminant is the part of the quadratic formula that is under the square root sign. A positive discriminant means that your answer will be a real number while a negative discriminant means you will have an imaginary number (since a negative number times a negative number always yields a positive number, in real life it is impossible to have a negative number under a square root sign).

The discriminant can be expressed as b^2-4ac for a quadratic equation in the form of ax^2+bx+c=0

Therefore for question letter a
a=1; b=4; c=-1 so 4^2-4(1)(-1) will yield a positive number so you will have two real roots

Ok, so now I will show you how to work the quadratic formula:
the formula is as follows (remembering what a, b, and c are again from above):

x=[-b +/- sqrt(b^2-4ac)]/2a

Solving for 3x^2-2x+5=0
a=3; b=-2; c=5
x=[2 +/- sqrt(4-4(3)(5)]/2(3)
x=[2 +/- sqrt(-56)]/6

I am not sure if you got this far in algebra class but for imaginary roots, we typically express them in terms of i, where i is equal to sqrt(-1). Therefore:
x=[2 +/- sqrt{(4)(2)(7)(-1)}]/6
x=[2 +/- sqrt(14)][2][i]/6= 1 +/- (sqrt[14])[i]/3=
{1 +/- (i)(sqrt[14] }/ 3 is your answer.

Try the others out to make sure you get the hang of it.

Answer 2

the discriminant is b^2 - 4ac. If this comes out negative, there are no real roots, just two complex ones because there are no real roots of negative numbers. If it comes out to be 0, there is one real root, because adding and subtracting 0 mean the same thing. If it is positive, there are 2 real roots.

To solve, plug in your values for a, b, and c from your equation in the form ax^2 + bx + c = 0 to the quadratic formula:

(-b +/- sqrt(b^2 - 4ac))/2a

5a) a=1, b=4, c=-1, so discriminant = 4^2 - 4(1)(-1) = 16 + 4 = 20, so there are 2 real roots.

6a) a=3, b= -2, c = 5, so (+2 +/- sqrt(4-4(3)(5))/2(3)
= (2 +/- sqrt (4 - 60))/6
= (2 +/- sqrt (-54))/6
You can break down sqrt (-54) into 3sqrt6 i if you are using complex numbers.
(2 +/- 3 sqrt6 i) / 6

Answer 3

1) When you have an equation in the form of ax^2 + bx + c = 0, the discriminant is b^2 - 4ac.

If the discriminant is less than 0, you have no real solutions.
If the discriminant is equal to 0, you have only one solution (or "two repeating solutions")
If the discriminant is greater than 0, you have two distinct (different) solutions.

2) The quadratic formula is x = [ -b ± √(b^2 - 4ac) ] /2a

Now that you know these, you should be able to do the problems.

Answer 4

to get a,b, c values, look at co-efficients of equation. So for your question
5.)a) x^2+4x-1=0

then a=1 b=4 and c=-1



-b± √b² - 4ac(divide by 2a)
-4± √4² - 4(1)(-1)(divide by 2x1)
-4± √16+4(divide all by 2)
-4± √20

x= -4+√20 and x=-4-√20

i just realised i solved that :| oopsie, but to determine the nature of the roots
beacuse: b2 – 4ac > 0 then the roots are real and irrational(as in this case because it is not a perfect square)

if b2 – 4ac > 0 and it forms a perfect square then the roots are real and rational.

if b2 – 4ac =0 then it has 1 real root

and for question 6 differenciate then equate to 0

Answer 5

The discriminant is the b^2 - 4ac that's in the quadratic formula. Since you have to do the square root of it, if it's negative there are complex (imaginary) roots; if it's zero the roots are rational and equal (since when you add zero you get the same as when you subtract it) ; if it's a positive perfect square such as 9 or 36 the roots are rational and unequal; if it's positive but not a perfect square like 8 or 32 the roots are irrational

Answer 6

If you have no idea what the discriminant of a quadratic is, or what the quadratic formula is, then you have no business being in an algera class that uses them. Ask that you be placed in a previous years class so that you can learn all of the things you failed to learn the 1'st time you took the class.

If you're studying on your own, you have gotten a book that's a bit too advanced and you need to find one that's more elementary and which explains the quadratic formula and discriminants.

Doug

Answer 7

to find the discriminant use the formula....answer= b squared minus 4ac.

Then if the number(answer) is over 0, it has 2 nature roots

if the number is 0, it has only 1

and if the number is below 0, no natural roots

the quadratic formula is --b plus or minus (square root) b squared minus 4ac....

but you i don't think you can use the quadratic formula to find the roots(if you got confused and don't get what i wrote, then go to google, write qaudratic formula, click on the wikipedia link and it has it right there, you can scroll down to find the formula for the discriminant too!)


:) hope this helps

Answer 8

x=5

Answer 9

discriminant is b^2 - 4ac

this is the part of the quadratic that is under the square root.
and see if you get a positive number, negative number, perfect square, zero and you know if you'll have one root, two roots, real roots, imaginary roots

Something like that

Answer 10

You must have taken the quadratic formula in class.
The discriminant comes after the plus & minus signs.