# NCERT Solutions, CBSE Sample paper, Latest Syllabus, NCERT Books, Last Year Question Papers and Many More ...

## Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x² – 2x – 8

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x² – 2x – 8

(i)

Factorize the equation

Compare the equation with ax²  + bx  + c  = 0
We get
a = 1 ,b=-2 c= -8
To factorize the value we have to find two value which
sum is equal to b                      =-2
and product is  a x c  = 1 x -8    = -8

2 and -4 are such number which

sum is 2-4        = - 2
product is 2*-4 = - 8

So we can write middle term -2 x  = 2 x – 4 x
We get
x²+2x-4x-8=0
x (x + 2)-4(x + 2) = 0
(x+2) (x-4)          = 0
First zero
x + 2                  = 0
x                        = -2
Second zero
x-4                   = 0
x                      = 4
sum of zero                -2 + 4    = 2
product of zero           2 x -4     = -8

For a equation ax² + bx  + c  = 0 , if  zeroare α and β ,

Plug the values of a , b and c we get
Sum  of zeros              -b/a     = -(-2/1)           = 2
Product of zeros          c/a      =-8/1               = -8

Question 1. Find the zeroes of the following quadratic polynomials and verify the relation