Question

Very-Short-Answer Questions

If the roots of the quadratic equation $px\left(x-2\right)+6=0$ are equal, find the value of p. [CBSE 2013]

Answer 1

It is given that the roots of the quadratic equation $p{x}^2-2px+6=0$ are equal.
$$\begin{gathered} \therefore D=0 \\ \Rightarrow {\left(-2p\right)}^2-4\times p\times 6=0 \\ \Rightarrow 4p^2-24p=0 \\ \Rightarrow 4p\left(p-6\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow p=0\mathrm{or}p-6=0 \\ \Rightarrow p=0\mathrm{or}p=6 \end{gathered}$$

For p = 0, we get 6 = 0, which is not true.

∴ p ≠ 0

Hence, the value of p is 6.