If the coefficient of x^2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Question

Is the following statement ‘True’ or ‘False’?Justify your answer.

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

Answer 1

True, because in this case discriminant is always positive.

For example, in ax²+ bx + c = 0, as a and c have opposite sign, ac < 0

⟹ Discriminant = b² – 4ac > 0.