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find the value of parameter a not equal to 0 for which one of the roots of the quadratic equation x^2-x+3a=0 is double one of the roots of equation x^2-x+a=0.

find the value of parameter a not equal to 0 for which one of the roots of the quadratic equation x^2-x+3a=0 is double one of the roots of equation x^2-x+a=0.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
let the roots of x^2-x+3a=0 be
2p and q respectively and the roots for x^2-x+a=0 be
p and r respectively.
then,
 
2p + q = 1
p + r  = 1
2pq = a
pr = 3a
solving all the above eqns. we get,
p = 5/11
q = 1/11
r = 6/11
and
a = 10/121.

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