First slide

Theory of expressions

Question

If the roots of $a x^{2} + b x + c = 0 (a > 0)$ be each greater than unity, then

Moderate

A

$a + b + c = 0$
B

$a + b + c > 0$
C

$a + b + c < 0$
D

none of these

Solution

Let $f (x) = a x^{2} + b x + c$ . Since $1$ lies outside the roots of $f (x) = 0 .$ So,
$a f (1) > 0$
$\Rightarrow f (1) > 0 \Rightarrow a + b + c > 0 [∵ a > 0]$

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