Question

Write whether the following statements are true or false. Justify your answers. (v) If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

• A. True
• B. False

Answer 1

The correct option is A True

Explanation.

Let us consider an example, in $a{x}^2+bx+c=0$, as $a$ and $c$ have opposite sign, $ac<0$

In this case, the discriminant is always positive.

Discriminant$=b^2–4ac>0$

Thus, if Discriminant$>0$ then the quadratic equation has real roots.

Hence, the given statement is True.