CAT 2022 Slot 2 QA Question & Solution

AlgebraMedium

Let r and c be real numbers. If r and -r are roots of $5x^{3} + cx^{2} - 10x + 9 = 0$, then c equals

$-\frac{9}{2}$

$\frac{9}{2}$

-4

Let the roots of the given equation $5x^{3} + cx^{2} - 10x + 9 = 0$ be r, -r and p

r - r + p = $-\frac{c}{5}$

p = $-\frac{c}{5}$ ...... (1)

$-r^2-pr+pr=-2$

$r^2=2$ ...... (2)

$-r^2p=-\frac{9}{5}$

$p=\frac{9}{10}$ ...... (3)

Substituting p in (1), we get

$\frac{9}{10}=-\frac{c}{5}$

$-\frac{9}{2}=c$

The answer is option A.