CAT 2022 Slot 2 Paper

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Question : 51 of 66

Marks: +1, -0

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

$9/{-2}$
$9/2$
$-4$
$4$

Solution:

Let the roots of the given equation

5 x^3+c x^2-10 x+9=0

be

{r},- {r}

and

p

{\r}- {\r}+ {\p}=-{c}/{5}

{\p}=-{c}/{5}

. . .(1)

-r^2-p r + p r=-2

r^2=2

. . .(2)

-r^2 p=-{9}/{5}

p={9}/{10}

... (3)

Substituting

p

in

\Eqs (1)

, we get

{9}/{10}=-{c}/{5}

-{9}/{2}=c

The answer is option A.

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