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
