Question

Find the zeros of the quadratic polynomial f(x)= x^2-2x-8 and verify the relationship between the zeros and their coefficients.

Answer 1

$\mathtt{{\colorbox{silver}{Solution}}}$

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 x²/Coefficient of x= 2

So, sum of zeros =α+β=−

Coefficient of x /Coefficient of x²

Now, product of zeros =αβ=(4)(−2)=−8

Also, product of zeros =

Constant term/ coefficient of x²= -8

∴ Product of zeros =

Constant term / coefficient of x² =αβ

Hence verified too!!