Question

If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ______ roots.

Answer 1

If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Explanation:

For ax² + bx + c = 0 with b = 0 we have ax² + c = 0 ⇒ `x^2 = -c/a`. If a and c have the same sign, then `c/a > 0` so `-c/a < 0`, so x² is negative and there is no real x the discriminant D = b² – 4ac = –4ac is negative.