find the value of c such that equation 4x² - 2(c + 1)x +(c + 4) = 0 has real and equal roots

The given quadratic equation is . It has real and equal roots.

∴ Discriminant of the given quadratic equation, D = 0

⇒ c (c – 5) + 3(c – 5) = 0

⇒ (c + 3) (c – 5) = 0

⇒ c + 3 = 0 or c – 5 = 0

⇒ c = – 3 or 5

Thus, the value of c is – 3 or 5.