Question

What is the positive value of k for which the equations x2 + kx + 144=0 and
x2-12x + k =0 will have real roots? ​

Answer 1

Answer:    16

Step-by-step explanation:

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≤−16For the second equation,64−4k≥0⇒ k≤16

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

∴Option D is correct.

Answer 2

Answer: 16

explanation:

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.