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

Let $a{x}^2+bx+c=0$ be a quadratic equation.

It is given that, coefficient of x² and the constant term of a quadratic equation have opposite signs
⇒ ac < 0
⇒ 4ac < 0
⇒ −4ac > 0
⇒ b² −4ac > 0
⇒ Discriminant > 0
⇒ Roots are real and distinct

Hence, 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.