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Let $a, b, c$ be real numbers such that $a+b+c < 0$ and the quadratic equation $a x^{2}+b x+c=0$ has imaginary roots. Then.
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The correct answer is:
$a < 0, c < 0$
Let $f(x)=a x^{2}+b x+c$
$\Rightarrow \quad f(1)=a+b+c < 0$
Again, $f(x)$ has imaginary zeros. So, $a < 0$. Also, $f(0)=c .$ since $f(x)$ is downward parabola. So, $c < 0$
$\Rightarrow \quad f(1)=a+b+c < 0$
Again, $f(x)$ has imaginary zeros. So, $a < 0$. Also, $f(0)=c .$ since $f(x)$ is downward parabola. So, $c < 0$
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