Question

Say true or false:

The quadratic polynomial $x^2+kx+k$ have equal zeroes for some odd integer $k>1.$

• A. True
• B. False

Answer 1

The correct option is B False

Given, the quadratic polynomial is
$p\left(x\right)=x^2+kx+k$.
Then the Discriminant (D) $=k^2-4k$.
We know that, for equal zeros/roots, $D=0$.
$=>k^2-4k=0$
$=>k(k-4)=0$
$=>k=0$ or $k=4$
Hence the quadratic polynomial can have equal zeros at $=>k=0$ or $k=4$. So, it cannot have equal zeros for any odd integer $k>1$.

Hence, the statement is false.

Therefore, option $B$ is correct.