Question

9. The positive value of K for which both the equations x2 + Kx + 64 =0 and X2-8x+K=0 have real roots, is ​

Answer 1

ANSWER

For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.

For the first equation,

k

2

−4(1)(64)≥0 (∵discriminant=b

2

−4ac)

⇒ k

2

−256≥0

⇒ (k−16)(k+16)≥0

⇒ k≥16 and k≤−16

For the second equation,

64−4k≥0

⇒ k≤16

∴ the value of k that satisfies both the conditions is k=16.