Question

If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the roots of the quadratic equation are ______ and ______.

Answer 1

If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the roots of the quadratic equation are real and distinct.

Explanation:

For ax² + bx + c = 0, the product of the roots is `c/a`, so if a and c have opposite signs then `c/a < 0` and the roots have opposite signs. Also ac < 0 makes the discriminant b² – 4ac positive, so the roots are real.