Question

The value of p for which the quadratic equation $2p{x}^2+6x+5=0$ has real and distinct roots is :

• A. $\frac{1}{2}$
• B. 1
• C. 2
• D. $\frac{9}{10}$

Answer 1

The correct option is A $\frac{1}{2}$

Given that the quadratic equation has real and distinct roots.
$\therefore D>0$
$\Rightarrow b^2-4ac>0$
Comparing the given equation with the standard form, we have a = 2p, b = 6 and c = 5

$\Rightarrow (6{)}^2-4(2p\left)\right(5)>0$
$\Rightarrow 36-40p>0$
$\Rightarrow 36>40p$
$\Rightarrow \frac{9}{10}>p$ and only $\frac{1}{2}<\frac{9}{10}$ (among the given options)