Question

Q. Find the positive values of k for which quadratic
equations x² + kx + 64 = 0 and x² - 8x + k = 0 both
will have the real roots.​

Answer 1

Correct option is

Correct option isD

Correct option isD16

Correct option isD16For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.

Correct option isD16For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.For the first equation,

Correct option isD16For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.For the first equation,k

Correct option isD16For a quadratic equation to have real roots, discriminant must be greater than or equal to zero.For the first equation,k 2

Correct option isD16For 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

Correct option isD16For 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

Correct option isD16For 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.

∴Option D is correct.