Question

Find c, if the quadratic equation x^2 – 2 (c +1)x + c^2 = 0 has real and equal roots.
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Answer 1

x^2 - 2(c+1)x + c^2 = 0

here, in this equation a = 1, b = -2(c +1),

c = c^2

Since, the equation has real and equal roots

D = 0

b^2 - 4ac = 0

[-2(c+1)]^2 - 4(1)(c^2) = 0

4(c+1)^2 - 4c^2 = 0

4(c^2 + 2c + 1) - 4c^2 = 0

4c^2 + 8c + 4 -4c^2 = 0

8c + 4 =0

4(2c + 1) = 0

2c+1 = 0

2c = -1

c= -1/2.

Hope it helps you.

Answer 2

it is -1/2

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