Question

Determine the positive value of 'k' for which the equation x²+kx+64=0 and x2-8x+k=0 will both have real and equal roots.

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Answer 1

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≤−16

For the second equation,

64−4k≥0

⇒ k≤16

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

Answer 2

Answer:

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