If the coefficient of x^2 and the constant term have the same sign and if the coefficient of x term is zero,

Question

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

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

Answer 1

True, because in this case discriminant is always negative.

For example, in ax²+ bx + c = 0, as b = 0, and a and c have same sign then ac > 0

⟹ Discriminant = b² – 4ac = – 4 a c < 0