Question

find the value of k so that the zeroes of the quadratic polynomial 3x^2-kx-14 are in ration 7;6

Answer 1

Let, p(x)=3x²-kx+14.
Also let that α, β are the roots of p(x). Then,
α+β=-(-k/3)=k/3 ----------(1) and
αβ=14/3 --------------------(2)
By the given question, α:β=7:6
or, α=7β/6
∴, from (2)
7β/6×β=14/3
or, β²=14/3×6/7

or, β²=4
or, β=+-2
Now from (1),
7β/6+β=k/3
or, (7β+6β)/6=k/3
or, 13β=k/3×6
or, 13β=2k
or, k=13β/2
When β=2,
k=(13×2)/2
or, k=13
When β=-2
k=(13×-2)/2
or, k=-13
∴, k=+-13