If the zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of $2x^2-5x-3$, find the value of $p$ and $q$.

Given: Zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of $2x^2-5x-3$.

To do: To find the vale of $p$ and $q$

Solution:

Let $\alpha$ and $\beta$ are the zeroes of the $2x^2-5x-3$.

Therefore, Sum of the zeroes $\alpha+\beta=-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\ ......\ ( i)$

Product of the zeroes $\alpha\beta=\frac{c}{a}=\frac{-3}{2}\ ......\ ( ii)$.

For polynomial $x^2+px+q$:

Zeroes will be $2\alpha$ and $2\beta$

Sum of the zeroes $2\alpha+2\beta=-\frac{p}{1}=-p$

$\Rightarrow 2( \alpha+\beta)=-p$

$\Rightarrow 2times\frac{5}{2}=-p$         [From $( i)\ \alpha+\beta=\frac{5}{2}$]

$\Rightarrow p=-5$

Product of the zeroes $2\alpha.2\beta=\frac{q}{1}$

$\Rightarrow 4\alpha\beta=q$

$\Rightarrow 4\times( -\frac{3}{2})=q$  [From $( ii)\ \alpha\beta=\frac{-3}{2}$]

$\Rightarrow q=-6$

Thus, $p=-54 and $q=-6$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

117 Views

Kickstart Your Career

Get certified by completing the course

Get Started