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