Question

Which of the following could be the value of $p$ , if the quadratic equation $2p{x}^2+6x+5=0$ has real and distinct roots?

• 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.
$\therefore$ Discriminant, $D>0$

Here, $a=2p,b=6$ and $c=5$

$\Rightarrow b^2-4ac>0$
$\Rightarrow (6{)}^2-4(2p\left)\right(5)>0$
$\Rightarrow 36-40p>0$
$\Rightarrow 36>40p$
$\Rightarrow \frac{9}{10}>p$

Among the options only $\frac{1}{2}<\frac{9}{10}.$