Question

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

Answer 1

x² – 4kx + k + 3 = 0 

Comparing the above equation with ax² + bx + c = 0, we get 

a = 1, b = – 4k, c = k + 3 

Let α and β be the roots of the given quadratic equation.

Then,  α + β = \(= \frac { -b }{ a } \) and αβ \(= \frac { c }{ a } \)

According to the given condition,

 α + β = 2αβ

∴ -(b/a) = 2c/a

∴ -b = 2c

∴ -(-4k) = 2(k = 3)

∴ 4k = 2k + 6         

∴ 4k - 2k = 6

∴ 2k = 6                 

∴ k=6/2

∴ k = 3