Question

If the quadratic equation $p{x}^2-2\sqrt{5}px+15=0$ has two equal roots then find the value of $p$.

Answer 1

If in equation $a{x}^2+bx+c=0$ the two roots are equal

Then $b^2-4ac=0$

In equation $p{x}^2-2\sqrt{5}px+15=0$

$a=p,b=-2\sqrt{5}pandc=15$

Then $b^2-4ac=0$

$\Rightarrow (-2\sqrt{5}p{)}^2-4\times p\times 15=0$

$\Rightarrow 20p^2-60p=0$

$\Rightarrow 20p(p-3)=0$

So when $p-3=0\Rightarrow p=3$

$p\ne 0$ as it makes coefficient of $x^2=0$

Hence, $p=3$