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