Question

If equations ax² + bx + c = 0 and x² + 2x + 3 = 0 have a common root, show that a:b:c = 1:2:3.

Answer 1

Since roots of equation x² + 2x + 3 = 0 are imaginary and equations x² + 2x + 3 = 0 and ax² + bx + c = 0 have a common root, both roots will be common. Hence, both equations are identical. Therefore,