Question

Find the value(s) of $p$ for which the quadratic equation $2x^2+3x-p=0$ has real roots.

Answer 1

The given quadratic equation is,

$2x^2+3x-p=0$

Here,

$a=2,b=3,c=-p$

If the equation is supposed to have real roots, then $D\ge 0$. Therefore,

$b^2-4ac\ge 0$

$9-4\times 2\times (-p)\ge 0$

$9+8p\ge 0$

$p\le \frac{9}{8}$

Thus, the values of $p$ for which the equation has real roots are $(-\infty ,\frac{9}{8}]$.