First slide

Theory of equations

Question

If $a, b, c, \in R$ and the equation $x^{2} + (a + b) x + c = 0$ has no real roots, then
$c (a + b + c)$ then more

Moderate

A

2
B

-2
C

0
D

none of these

Solution

We have $f (x) = x^{2} + (a + b) x + c > 0 \forall x \in R$
Thus, $f (0) > 0, f (1) > 0$
$\Rightarrow c (a + b + c) > 0$

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