Question

For what value of k are the roots of the quadratic equation `kx(x - 2sqrt(5)) + 10 = 0` real and equal?

Answer 1

The given equation is 

`kx(x - 2sqrt(5)) + 10 = 0` 

⇒ `kx^2 - 2sqrt(5)kx + 10 = 0` 

This is of the form ax² + bx + c = 0, where a = k, b = `-2sqrt(5)k` and c = 10

∴ D = b² – 4ac

= `(-2sqrt(5)k)^2 - 4 xx k xx 10`

= 20k² – 40k

The given equation will have real and equal roots if D = 0. 

∴ 20k² – 40k = 0 

⇒ 20k(k – 2) = 0 

⇒ k = 0 or k – 2 = 0 

⇒ k = 0 or k = 2 

But, for k = 0 we get 10 = 0, which is not true

Hence, 2 is the required value of k.