# Write all the values of p for which the quadratic equation x^2 + px + 16 = 0

Quadratic Equations (C10)
Write all the values of p for which the quadratic equation x^{2} + px + 16 = 0 has equal roots. Find the roots of the equation so obtained.

### Answer

x^{2} + px + 16 = 0 have equal roots if D = 0

D = p^{2} – 4(16)(1) = 0

p^{2} = 64

⇒ p = ±8

∴ x^{2} ± 8x + 16 = 0

⇒ (x ± 4)^{2} = 0

x ± 4 = 0

∴ Roots are x = –4 and x = 4.