Question

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.

Answer 1

3x² – 8x – (2k + 1) = 0

α = 7β   ...(Given)

α + β = `- (-8)/3 = 8/3`

7β + β = `8/3`

`\implies` β = `1/3`

αβ = `(-(2k + 1))/3`

7ββ = `(-(2k + 1))/3`

`7 xx 1/9 = (-(2k + 1))/3`

7 = – 6k – 3

k = `10/(-6) = (-5)/3`

∴ k = `(-5)/3`