Question

find the values of p for which the equation has equal roots (p+4)x^2 + (p+1)x +1=0​

Answer 1

on comparing

(p + 4)x² + (p + 1)x + 1 = 0

with ax² + bx + c = 0

a = p + 4

b = p + 1

c = 1

since the equation has equal roots

b² - 4ac = 0

(p + 1)² - 4(p + 4)(1) = 0

p² + 2p + 1 - 4p - 16 = 0

p² - 2p - 15 = 0

p² - 5p + 3p - 15 = 0

p(p - 5) + 3(p - 5) = 0

(p + 3)(p - 5) = 0

p + 3 = 0 or p - 5 = 0

p = -3 or p = 5