Question

If the equations ax^2 + bx + c =0 and x^2 + 2x + 9 =0 have a common root then find a:b:c

Answer 1

The roots of the equation x² + 2x + 9 =0 are imaginary  as the discriminant D= 4-36= -32 , which is negative.

As the imaginary roots of a quadratic equation are conjugate to each other, so both the roots of the equations will be common.

So, a/1 = b/2 =c/9

or,  a:b:c = 1:2:9