Question

11. If x=1 is a common root of ax? + ax + 2 = 0 and x2 + x + b =0, then the value of ab is
x=to ax2 + ax +2=0 x2 + x + b = 0 & Boat abes​

Answer 1

Answer:

Roots of ax

2

+2bx+c=0 are x=

2

−2b±

4b

2

−4ac

=−b±

b

2

−ac

And roots of px

2

+2qx+r=0 are x=

2

−2q±

4q

2

−4pr

=−q±

q

2

−pr

Now, we know that irrational roots of quadratic occurs in a pair i.e. if roots will be irrational then both of roots of above quadratics may be common

Hence for only and only root to be common we must have both quadratics roots rational.

And for that we must have b

2

−ac and q

2

−pr a perfect square