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in Quadratic Equations by (31.2k points)
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The positive value of k for which the equation x2 + kx + 64 = 0 and x2 – 8x + k = 0 will both have real roots, is 

A.

B.

C. 12 

D. 16

1 Answer

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by (30.8k points)
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Best answer

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

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