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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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