Question

If the quadratic equation `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots then find the value of p.

Answer 1

It is given that the quadratic equation `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots.

∴ D = 0 

⇒ `(-2sqrt(5)p)^2 - 4 xx p xx 15 = 0` 

⇒ 20p² – 60p = 0

⇒ 20p(p – 3) = 0 

⇒ p = 0 or p – 3 = 0 

⇒ 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.