Question

The value c which the quadratic equation 4x^2-2(c+1)x +(c+1) =0hws equal roots

Answer 1

Answer:

Your answer in in the picture

Answer 2

This is nothing but one equation and one variable case. Which means we have one variable c and the equation give that both roots are same.

First of all for an equation A$x^{2}$ + Bx + C = 0

The roots are [- B + √(B² - 4AC) ] / 2A and [- B - √(B² - 4AC) ] / 2A

From given equation, A = 4 , B = -[2(c+1)] , C = c+1 ------- 1

So give equality of roots, our equation becomes,

[- B - √(B² - 4AC) ] / 2A = [- B + √(B² - 4AC) ] / 2A

Simplifying cancelling 2A and -B, we have

2√(B² - 4AC) = 0

B² = 4AC

From 1

4(c+1)² = 16 (c+1)

c+1 = 4

c = 3

So, there is the answer, c= 3