Question

find the value of K so that the quadratic equation x2-4kx+k=0 has equal roots.

Answer 1

hope it's helpful for you

Answer 2

Answer:

A quadratic equation $ax^2+bx+c=0$  ....[1] has equal roots when discriminant is 0.

Discriminant is given by:

$\text{Discriminant D} = \sqrt{b^2-4ac}$

As per the equation:

Given the quadratic equation: $x^2-4kx+k =0$

On comparing with [1] we have;

a = 1 , b = -4k and c = k

Since, the given quadratic equation has equal root

⇒D =0

$\sqrt{b^2-4ac} = 0$

Squaring both sides we have;

$b^2-4ac = 0$

⇒$b^2 =4ac$

Substitute the given values we have;

$(-4k)^2=4 \cdot 1 \cdot k$

Simplify:

$16k^2 =4k$

Divide both sides by 4k we have;

$4k = 1$

or

$k = \frac{1}{4}$

therefore, the value of k is, 1/4