Question

Find K if one root of the quadratic equation is 5 times the other ?

Answer 1

Answer:

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

Hope it will help u