Question

Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients,
x^2-2x-8​

Answer 1

Answer:

f(x)=x2−2x−8

⇒f(x)=x2−4x+2x−8

⇒f(x)=x(x−4)+2(x−4)]

⇒f(x)=(x−4)(x+2)

Zeros of f(x) are given by f(x) = 0

⇒x2−2x−8=0

⇒(x−4)(x+2)=0

⇒x=4 or x=−2

So, α=4 and β=−2

∴ sum of zeros =α+β=4−2=2

Also, sum of zeros =Coefficient of x2Coefficient of x

=1−(−2)=2

So, sum of zeros =α+β=−Coefficient ofx2Coefficient of x

Now, product of zeros =αβ=(4)(−2)=−8

Also, product of zeros =Coefficient ofx2Constant term

=1−8=−8

∴ Product of zeros =Coefficient of x