1. If one root
of the quadratic equation kx2 – 5x + 2 = 0 is 4 times the
other, find k.
Sol. kx2 – 5x + 2 = 0
Comparing with ax2 + bx + c =
0 we have a = k, b = – 5, c = 2
Let α and β be the roots of given quadratic equation.
α = 4 β [Given]
∴ α +β = - b/a = - (- 5)/k
= 5/k
∴ 4β + β = 5/k
∴ 5β = 5/k
∴ β = 5/5k
∴ β = 1/k
Also, α.β =
c/a = 2/k
∴ 4β .β = 2/k
∴ 4(1/k)(1/k) = 2/k
∴ 4/k2 =
2/k
∴ 4/2 = k2/k
∴ 2 = k
