If a, b, c, a(1), b(1), c(1) are rationa...

If a, b, c, `a_(1), b_(1), c_(1)` are rational and equations `ax^(2) +2bx+ c= 0 and a_(1)x^(2) +2b_(1)x+c_(1)=0` have one and only one root in common, then

A

both `b^(2)-ac and b_(1)^(2)-a_(1)c_(1)` may not be perfect squares

B

both `b^(2)-ac and b_(1)^(2)-a_(1)c_(1)` must be perfect squares

C

at least one of `b^(2)-ac and b_(1)^(2)-a_(1)c_(1)` must be perfect squares

D

cannot say anything

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

The equations x^( 5) + ax + 1 = 0 and x^( 6) + ax^(2) + 1 = 0 have a common root. Then a is equal to

If b_(1)b_(2)= 2(c_(1)+c_(2)) , then prove that at least one of the equations x^(2) +b_(1)x+c_(1)=0 and x^(2) +b_(2)x+ c_(2)=0 has real roots.

If the equations x^(2) + ax+1=0 and x^(2)-x-a=0 have a real common root b, then the value of b is equal to

For a ne b, if the equation x ^(2) + ax + b =0 and x ^(2) + bx + a =0 have a common root, then the value of a + b equals to: