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The quadratic equations x^2""-""6x""+"...

The quadratic equations `x^2""-""6x""+""a""=""0""` and `""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

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
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`.
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