Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively $4,1$.

Answer 1

Find the sum and product of the roots of the quadratic equation.

Let $\alpha$ and $\beta$ be the roots of a quadratic equation.

Sum of the zeroes

$\Rightarrow \alpha +\beta =4$

Product of the zeroes

$\Rightarrow \alpha \beta =1$

Substitute these values in the quadratic equation $x^2-\left(\alpha +\beta \right)x+\alpha \beta =0$.

$\Rightarrow x^2-4x+1=0$

Hence, the quadratic equation is $x^2-4x+1=0$.