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

Given:

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.

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 same signs, then $ac>0$

This implies,

$D=(0)^2 - 4ac$

$=-4ac<0$

The discriminant is always negative, so it has no real roots.

Hence, the given statement is true.

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