Question

Write whether the following statements are true or false. Justify your answers.

If the coefficient of $x^2$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.

• A. True
• B. False

Answer 1

The correct option is A True

Explanation.

Let us consider quadratic equation $a{x}^2+bx+c=0$ as $b=0$, and $a$ and $c$ have same sign then $ac>0$

In this case discriminant is always negative.

Discriminant

$$\begin{gathered} =b^2–4ac \\ =–4ac<0 \end{gathered}$$

If Discriminant$<0$ then the quadratic equation has no real roots.

Hence the given statement is True.