Question

Find the value of k if the roots of x²+kx+12=0 are in the ratio of 1:3.

Answer 1

Hey Mate ☺

Here is your solution :-

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Let the two roots be α and β
Given α : β = 1 : 3
That is α / β = 1 / 3
β = 3 α
Given quadratic equation is x^2+kx+12=0
Sum of roots (α + β) = -b/a = - k
That is (α + 3 α) = - k
Hence α = - k/4 ---- (1)
Product of roots, (αβ) = c/a = 12/1
That is (3α^2) = 12
α^2 = 4
α = ± 2
Equation (1) becomes,
2 = - k/4
Hence k = -8
If α = - 2
k = 8

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Hope it helps ☺