Question

Find the value of $p$ in the equation, where the roots are real,
$5x^2+3x-p=0$

• A. $p\le \frac{20}{9}$
• B. $p\ge \frac{9}{20}$
• C. $p\ge \frac{-9}{20}$
• D. None

Answer 1

Answer: (C)

$p\ge \frac{-9}{20}$

Given equation is $5x^2+3x-p=0$

For real roots $\Delta \ge 0$ i.e. $b^2-4ac\ge 0$
Here $a=5,b=3,c=-p$
Therefore, ${\left(3\right)}^2-4\left(5\right)(-p)\ge 0$
$\Rightarrow 9+20p\ge 0$
$\Rightarrow 20p\ge -9$
$\Rightarrow p\ge \frac{-9}{20}$