Question

Find c, if the roots of the quadratic equation x² – 2(c + 1)x + c² = 0 has real equal roots.

Answer 1

Given: x² – 2(c + 1)x + c² = 0
First, we need to find the discriminant of the given quadratic equation.
We know that the discriminant of a quadratic equation is Δ = b² – 4ad
On comparing the given equation with ax² + bx + d = 0 in variable x, we get:
a = 1, b = –2(c + 1), d = c²
Thus,
Δ = (–2(c + 1))² – 4(1)(c²)
=> Δ = 4(c² + 1 + 2c) – 4c²
=> Δ = 4c² + 4 + 8c – 4c²
=> Δ = 4 + 8c
Since the roots of the given quadratic equation are real and equal, Δ = 0.
Thus, 4 + 8c = 0
=> c = $\frac{-4}{8}=\frac{-1}{2}$