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The quadratic eqns x^2-6x+a=0 and x^2-cx+6=0.The other roots of the first and second eqns. are integers in the ratio 4:3.Then the common root is ?

The quadratic eqns x^2-6x+a=0 and x^2-cx+6=0.The other roots of the first and second eqns. are integers in the ratio 4:3.Then the common root is ?

Grade:12th pass

2 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
10 years ago
Let the other roots be 4k, 3k
There for the roots of x^2 - 6x + a = 0 would be p, 4k and that of x^2 - cx + 6 = 0 would be p, 3k
there fore
p + 4k = 6
p*3k = 6
k = 2/p
hence: p + 8/p = 6
p^2 - 6p + 8 = 0
there fore p = 4 or 2


Thanks and Regards
Pratik Tibrewal
askiitians faculty
BTech
SKS
40 Points
10 years ago
If both 4 and 2 are there in options, then which one to choose ?

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