Question

$-4$ and $9$ are the sum and product of the zeros respectively of a quadratic polynomial. Find the quadratic polynomial.

Answer 1

We know that the formula for a quadratic polynomial is:

$p\left(x\right)=x^2-($Sum of the zeroes$)x+($Product of the zeroes$)=0$

We are given that the sum of the zeroes is $-4$ and the product of the zeroes is $9$, therefore, following the above formula, the required quadratic polynomial is:

$p\left(x\right)=x^2-(-4)x+9=x^2+4x+9$

Hence, the quadratic polynomial is $x^2+4x+9$.