Question

alpha and beta are zeros of a quadratic polynomial such that alpha + beta is equal to 24 and Alpha minus beta is equal to 8 find the quadratic polynomial having alpha and beta its zeros

Answer 1

_24and _8 it is the answer of your choice

Answer 2

The value of the quadratic polynomial having α = 16 & β = 8.

Solution:

Given:

$\begin{array}{l}{\alpha+\beta=24 \ldots \ldots \ldots(1)} \\ {\alpha-\beta=8 \quad \ldots \ldots \ldots(2)}\end{array}$

To find out the value we need to solve the above two equation by adding them as under:

$\begin{array}{l}{2 \alpha=32} \\ {\alpha=16}\end{array}$

Replacing the value of α = 16 in the equation (1),

$\begin{array}{l}{\alpha+\beta=24} \\ \\ {16+\beta=24} \\ \\ {\beta=24-16} \\ \\ {\beta=8}\end{array}$

Hence, the value of $\alpha=16\ \&\ \beta=8$

As alpha and beta are the zeros of quadratic polynomial, we can mention as under:

$\mathrm{p}(\mathrm{x})=\mathrm{x}^{2}-(\alpha+\beta) \mathrm{x}+\alpha \beta$

$\mathrm{p}(\mathrm{x})=\mathrm{x}^{2}-(16+8) \mathrm{x}+16(8)$

$\mathrm{p}(\mathrm{x})=\mathrm{x}^{2}-24 \mathrm{x}+128$.