Question:
Very-Short-Answer Questions
If the quadratic equation $p x^{2}-2 \sqrt{5} p x+15=0$ has two equal roots then find the value of $p$.
Solution:
It is given that the quadratic equation $p x^{2}-2 \sqrt{5} p x+15=0$ has two equal roots.
$\therefore D=0$
$\Rightarrow(-2 \sqrt{5} p)^{2}-4 \times p \times 15=0$
$\Rightarrow 20 p^{2}-60 p=0$
$\Rightarrow 20 p(p-3)=0$
$\Rightarrow p=0$ or $p-3=0$
$\Rightarrow p=0$ or $p=3$
For p = 0, we get 15 = 0, which is not true.
∴ p ≠ 0
Hence, the value of p is 3.