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Question
Sum of the roots of a quadratic equation is double their product. Find k if equation x2 – 4kx + k + 3 = 0
Solution
Let the root be α and β
According to the given condition
α + β = 2 α.β
α + β = `(-b)/a` αβ = `c/a`
`(-b)/a` = 2 `c/a`
- b = 2c ...(i)
Compare with ax2 + bx + c = 0
x2 - 4kx + k + 3 = 0
a = 1, b = -4k, c = k + 3
Substituting the values in equation (i)
-b = 2c
-(-4k) = 2 (k + 3)
∴ 4k = 2k + 6
∴ 4k - 2k = 6
∴ 2k = 6
∴ k = `6/2`
∴ k = 3
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