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

Given: Quadratic equation $px^{2}-2\sqrt{5}x+15=0$ has two equal roots.

To do: To find the value of $p$

Solution: 

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

On comparing it to $ax^{2}+bx+c=0$, we have

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

As known for equal roots, its discriminant should be zero.

$\Rightarrow D=b^{2}-4ac=0$

$\Rightarrow (2\sqrt{5})^{2}-4\times p\times15=0$

$\Rightarrow 20-60p=0$

$\Rightarrow 60p=20$

$\Rightarrow p=\frac{20}{60}$

$\Rightarrow p=\frac{1}{3}$

Thus, $p=\frac{1}{3}$

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Updated on: 10-Oct-2022

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