Question

Find the value of $p$ in the equation $2x^2+3x-p=0$ if the roots are real and equal.

Answer 1

Given quadratic equation $2x^2+3x-p=\mathrm{0......}\left(i\right)$
where $a=2,b=3,c=-p$
If the roots of the equation are equal then the descriminant $D=0$
$\Rightarrow$ $\sqrt{b^2-4ac}=0$
$\Rightarrow$ $3^2-4\times 2\times (-p)=0$
$\Rightarrow$ $9+8p=0$
$\Rightarrow$ $8p=-9$
$\Rightarrow$ $p=-\frac{9}{8}$