Question

Find the value of $p$ for which the given equation has real roots.
$8x^2+5x-2p=0$

• A. $p\ge \frac{-25}{64}$
• B. $p\le \frac{64}{25}$
• C. $p\ge \frac{25}{64}$
• D. None

Answer 1

The correct option is A $p\ge \frac{-25}{64}$

Given equation is $8x^2+5x-2p=0$

Here $a=8,b=5,c=-2p$

For real roots $\Delta \ge 0,b^2-4ac\ge 0$
Thus ${\left(5\right)}^2-4\left(8\right)(-2p)\ge 0$
$\Rightarrow 25+64p\ge 0$
$\Rightarrow 64p\ge -25$
$\Rightarrow p\ge \frac{-25}{64}$