Question

Find the value of p for which the roots of the equation px (x − 2) + 6 = 0 are equal.

Answer 1

px (x − 2) + 6 = 0
⇒px² − 2px + 6 = 0
Since, we know that for the equal roots in a quadratic equation, we have
$$\begin{gathered} D=0 \\ \Rightarrow b^2-4ac=0 \\ \Rightarrow {\left(-2p\right)}^2-4p\times 6=0 \\ \Rightarrow 4p^2-24p=0 \\ \Rightarrow 4p\left(p-6\right)=0 \\ \Rightarrow p-6=0\left[\because p\ne 0\right] \\ \Rightarrow p=6 \end{gathered}$$
Hence, the value of p is 6.