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Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

If the sum of the roots of the equation $x^2 + 8x + 2 - k = 0$ is twice the product of the roots.
Then find k.

Option:
A. 2
B. 4
C. 8
D. 6
Answer: D . 6

Justification:

Suppose the roots of the equation $x^2 + 8x + 2 - k = 0$ be α and β such that α < β.
Here, a = 1, b = 8 and c = 2 - k
.`.$α + β = {-b}/a = -8$
   and
.`.$αβ = c/a = {2 - k}/1 = 2 - k$
Here, the sum of the roots is double the product of the roots.
.`. α + β = 2αβ
.`. - 8 = 2(2 - k)
.`. - 4 = (2 - k)
.`. k = 6

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