Question

Sum of the roots of a quadratic equation is double their product. Find k if equation x² – 4kx + k + 3 = 0

Answer 1

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