Question

If a and b are the roots of the equation x² – kx + 16 = 0 and satisfy a² + b² = 32, then the value of k is …..

(a) 10 

(b) -8 

(c) (-8, 8) 

(d) 6

Answer 1

(c) -8, 8

a + b = k ….(1) 

ab = 16 ….(2)

a² + b² = (a + b)² – 2ab = 32.

k² – 32 = 32 ⇒ k² = 64 ⇒ k = ±8