If $a x^{2} + b x + c = 0$ has no real roots and $a + b + c < 0$ , then

c > 0

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c < 0

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c = 0

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Cannot say.

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Solution

The correct option is D $c < 0$
Let $f (x) = a x^{2} + b x + c$
Given $f (1) < 0$ and $f (x) = 0$ has no real roots, then we can say that $f (x) < 0$ for all $x$ .
So, $f (0) < 0$ .
So, we get $c < 0$ .

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