The quadratic equations `x^2""6x""+""a""=""0""a n d""x^2""c x""+""6""=""0` have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2

Options

A. 4
B. 3
C. 2
D. 1

Answer

C

Explanation

Let `alpha, 4 beta` be roots of `x^(2)-6x+a=0` and `alpha, 3beta` be the roots of `x^(2)-cx+6=0`
Then `alpha+4beta=6` and `4alpha beta=a`…I
`alpha+3beta=c` and `3alpha beta=6`.ii
From Eq I and ii we get
`a=8, alpha beta=2`
Now first equation becomes
`x^(2)-6x+8=0`
`impliesx=2,4`
If `alpha-2, 4beta=4,` then `3 beta=3`
If `alpha=4, 4 beta=2` then `3beta=3/2`
`:.` Common root is `x=2`.