CTET 2 Math and Science 7 Jan 2022 Paper

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Question : 37 of 150

Marks: +1, -0

What is the coefficient of

{\x}^2

in the product of

(\;{2}/{3} x^2+\;{5}/{4} x-3)

and

(3 x^2+4 x+1) ?

$\;{77}/{12}$
$-\;{10}/{3}$
$\;{43}/{4}$
$-\;{5}/{6}$

Solution:

⇒(2 x^2 \/ 3+5 x \/ 4-3) ×(3 x^2+4 x+1)

⇒ 2 x^2 \/ 3(3 x^2+4 x+1)+5 x \/ 4(3 x^2+4 x+1)+1(3 x^2+4 x+1)

⇒ 6 x^4 \/ 3+8 x^3 \/ 3+2 x \/ 3+15 x^3 \/ 4+20 x^2 \/ 4+5 x \/ 4+9 x^2+4 x+1

⇒ x^2 \;\text " is the coefficient "\;

⇒ 20 x^2 \/ 4+2 x^2 \/ 3-9 x^2

⇒-40 x^2 \/ 12=-10 x^2 \/ 3

∴

The value is

-10 \/ 3

.

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