The positive value of k for which the equation x2 + kx + 64 = 0 and x2 – 8x + k = 0 will both have real roots, is
If the given equation x2 + kx + 64 has real roots then D ≥ 0
D = b2 – 4ac ≥ 0
Here a = 1, b = k, c = 64
d = K2 – 4 (1) (64) ≥0
d = K2 – 256 ≥ 0
K ≥ 16…… (1)
If the given equation x2 – 8x + k = 0 has real roots then then
d≥0
D = b2 – 4ac ≥0
82 – 4(1) (k) ≥0
64– 4k ≥ 0
64 ≥ 4k
K ≤ 16…… (2)
From (1) and (2) we can conclude that k = 16