Question

Find the values of k for roots are real and equal in equation:

kx² – 2√5x + 4 = 0

Answer 1

The given equation kx² – 2√5x + 4 = 0 is in the form of ax² + bx + c = 0

Where a = k, b = – 2√5, c = 4

For the equation to have real and equal roots, the condition is

D = b² – 4ac = 0

⇒ (- 2√5)² – 4(k)(4) = 0

⇒ 20 –16k = 0

⇒ k = \(\frac{5}{4}\)

The value of k is \(\frac{5}{4}\).