Find k, if the sum of the roots of the quadratic equation 4x2 + 8kx + k + 9 = 0 is equal to their product.

5. Find k, if the sum of the roots of the quadratic equation 4x² + 8kx + k + 9 = 0 is equal to their product.

Sol. 4x² + 8kx + k + 9 = 0

Comparing with ax² + bx + c = 0 we have a = 4, b = 8k, c = k + 9

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

α + β  = α β  ......(i) [Given]

(i.e.) –b/a  = c/a 

∴ ^{- 8k}/⁴ = ^(k+9)/₄

∴ -8k = k+9

∴ -8k – k = 9

∴ - 9k = 9

∴ k = 9/-9

∴ k = -1