Question

If sum of the squares of zeroes of the quadratic polynomial$f\left(x\right)=x^2-8x+k$ is 40, find the value of K.

Answer 1

Let a and b be the zeroes of the polynomial $f\left(x\right)=x^2-8x+k$. Then,

$a+b=-\left(\frac{-8}{1}\right)=8$ and $ab=\frac{K}{1}=K$

It is given that

$a^2+b^2=40$

$=(a+b{)}^2-2ab=40$

$=8^2-2K=40$

$=2K=64-40$

$K=12$