Question

Find a quadratic polynomial, the sum of whose zeroes is $4$ and one zero is $5$.

Answer 1

Put the sum and product values of two roots of the quadratic equation.

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

Given, $\alpha +\beta =4$ and one of the zeroes is $5$.

Let $\alpha =5$. So,

$\begin{array}{rcl}5+\beta & =& 4\\ \beta & =& -1\end{array}$

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

$$\begin{gathered} \Rightarrow x^2-4x+\left[5\left(-1\right)\right]=0 \\ \Rightarrow x^2-4x-5=0 \end{gathered}$$

Hence, the quadratic equation is $x^2-4x-5=0$.