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algebra senior

Problem

The values of

k

for which the equation

2 x^{2} - k x + x + 8 = 0

will have real and equal roots are:

(A)

9 an d - 7

(B)

o n l y - 7

(C)

9 an d 7

(D)

- 9 an d - 7

Solution

b^{2} - 4 a c = 0 ⟹ b^{2} = 4 a c ⟹ (1 - k)^{2} = 4 (2) (8) ⟹ (1 - k)^{2} = 8^{2} ⟹ 1 - k = 8 ⟹ k = - 7, 1 - k = - 8 ⟹ k = 9

,

9 and - 7

Final answer

A