Question:
Very-Short-Answer Questions
If the roots of the quadratic equation $p x(x-2)+6=0$ are equal, find the value of $p$.
Solution:
It is given that the roots of the quadratic equation $p x^{2}-2 p x+6=0$ are equal.
$\therefore D=0$
$\Rightarrow(-2 p)^{2}-4 \times p \times 6=0$
$\Rightarrow 4 p^{2}-24 p=0$
$\Rightarrow 4 p(p-6)=0$
$\Rightarrow p=0$ or $p-6=0$
$\Rightarrow p=0$ or $p=6$
For p = 0, we get 6 = 0, which is not true.
∴ p ≠ 0
Hence, the value of p is 6.