If the quadratic equation $px^{2} -2\sqrt{5} px+15=0$ has two equal roots then find the value of $p$.
Given: The quadratic equation $px^{2}-2\sqrt{5}px+15=0$ has two equal roots.
To do: To find the value of P.
Solution:
The quadratic equation $px^{2}-2\sqrt{5}px+15=0$,
On comparing it to the standard quadratic equation $ax^{2}+bx+c=0$
We have $a=p, b=2\sqrt{5}p$, $c=15$
For equal roots its discriminant , $D=0$ or $b^{2}-4ac=0$
$\left( 2\sqrt{5} p\right)^{2} -4\times p\times 15=0$
$20p^{2} -60p=0$
$20p( p-3) =0$
$p( p-3) =0$
$\Rightarrow p=0,\ 3$
But, $p = 0$ is not possible.
Thus for $p=0,\ 3$ the given equation has two equal roots.
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