Quadratic Equations (C10)

Write all the values of p for which the quadratic equation x2 + px + 16 = 0 has equal roots. Find the roots of the equation so obtained.

Answer

x2 + px + 16 = 0 have equal roots if D = 0

D = p2 – 4(16)(1) = 0

p2 = 64

⇒ p = ±8

∴ x2 ± 8x + 16 = 0

⇒ (x ± 4)2 = 0

x ± 4 = 0

∴ Roots are x = –4 and x = 4.