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

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

Given:

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

To do:

We have to find whether the given statement is true or false.

Solution:

In a quadratic equation $ax^2+bx+c = 0$, if $a$ and $c$ have opposite signs, then $ac<0$

This implies,

$D=b^2 – 4ac > 0$

The discriminant is always positive, so it always has real roots.

Hence, the given statement is true.

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