Question

If – 4 is a root of the equation x² + px – 4 = 0 and if the equation x² + px + q = 0 has equal roots, find the values of p and q.

Answer 1

f(x) = x² + px – 4 = 0

If – 4 is a root, then

f(– 4) = (– 4)² + P(– 4) – 4

= 16 – 4p – 4 = 0

12 – 4p = 0

– 4p = – 12

p = 3

x² + 3x + q = 0 has equal roots,

∆ = b² – 4ac = 0

3² – 4 × 1 × q = 0

9 – 4q = 0

– 4q = – 9

q = `9/4`

p = 3, q = `9/4`