What is th Quadratic Formula?

Question

What is the exact Quadratic Formula? I really need to have the exact answer...I need to have my perfect answer...in my ASSIGNMENT........

Answer 1

If ax² + bx + c = 0
x = [ - b ± √(b² - 4ac) ] / 2a
Example
2x² - 3x + 1 = 0
x = [3 ± √(9 - 8)] / 4
x = [ 3 ± √1 ] / 4
x = 4 / 4 , x = 2 / 4
x = 1 , x = 1 / 2
Check
(2x - 1)(x - 1) = 0
x = 1 / 2 , x = 1

Answer 2

Quadratic formula is the formula give for equation
ax^2+bx+c =0

u use this when you are unable to get the value of x by factor method...

the formula is as follows

D = b^2-4ac

where
D is called the discriminant
b is the coeeficient of x
a is the coefficient of x^2
c is the constant value

If D<0 then you will not be able to solve the eqn at this level because at this level you would be unaware of solving sqrt(-1) ,,the root will be imaginary

If D>0 then roots of the equation will be unequal and real

if D=0 then roots will be real and equal

now you have found the value of D

put it in the formula

x = (-b +- sqrt(D))/2a

+- means you have to take two case one with +ve sign and another with -ve sign

the two values of x are also caled the roots of eqn.

the answer of your question is up this line.. after that there is a trick to check your answer...

Let alpha be the first value you calculated from the above formula
Let beta be the second value you calculated from the above formula

then

alpha + beta = -b/a
alpha * beta = c/a

this trick might not be told to you...but it is written in all the old sylabus books

Answer 3

question form a million : For this equation x^2 - 17*x + seventy two = 0 , answer right here questions : A. discover the roots employing Quadratic formulation ! answer form a million : The equation x^2 - 17*x + seventy two = 0 is already in a*x^2+b*x+c=0 sort. so we are in a position to advise that the fee of a = a million, b = -17, c = seventy two. 1A. discover the roots employing Quadratic formulation ! Use abc formulation and you get the two x1 = (-b+sqrt(b^2-4*a*c))/(2*a) or x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had be attentive to that a = a million, b = -17 and c = seventy two, we merely ought to subtitute the fee of a,b and c interior the abc formulation. Which produce x1 = (-(-17) + sqrt( (-17)^2 - 4 * (a million)*(seventy two)))/(2*a million) and x2 = (-(-17) - sqrt( (-17)^2 - 4 * (a million)*(seventy two)))/(2*a million) which will properly be grew to become into x1 = ( 17 + sqrt( 289-288))/(2) and x2 = ( 17 - sqrt( 289-288))/(2) Which make x1 = ( 17 + sqrt( a million))/(2) and x2 = ( 17 - sqrt( a million))/(2) So we get x1 = ( 17 + a million )/(2) and x2 = ( 17 - a million )/(2) So we've the solutions x1 = 9 and x2 = 8

Answer 4

Lets have an equation for example,
x^2 + 5x + 1 = 0

The formula would be
x = (-b±√(b^2-4ac))/2a

In this case,
a = 1; b = 5; c = 1

x = (-(5) ± √(5^2-4(1)(1)))/(2(1))
= (-5 ± √21)/2
= (-5 + √21)/2 or (-5 - √21)/2
= -0.2087 or -4.7913

Answer 5

Quadratic Formula

x = - b ± √ (b² - 4ac) / 2a

Answer 6

x = -b + or - the square root of (b^2 - 4ac) all over 2a

Answer 7

negative B plus or minus the square root of (B squared minus 4AC) divided by 2A