Question

Very-Short-Answer Questions

If the quadratic equation $p{x}^2-2\sqrt{5}px+15=0$ has two equal roots then find the value of p. [CBSE 2015]

Answer 1

It is given that the quadratic equation $p{x}^2-2\sqrt{5}px+15=0$ has two equal roots.

$$\begin{gathered} \therefore D=0 \\ \Rightarrow {\left(-2\sqrt{5}p\right)}^2-4\times p\times 15=0 \\ \Rightarrow 20p^2-60p=0 \\ \Rightarrow 20p\left(p-3\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow p=0\mathrm{or}p-3=0 \\ \Rightarrow p=0\mathrm{or}p=3 \end{gathered}$$

For p = 0, we get 15 = 0, which is not true.

∴ p ≠ 0

Hence, the value of p is 3.