CTET 2 Math and Science 3 Jan 2022 Paper

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Question : 39 of 150

Marks: +1, -0

If

10 x^2+x-3=(a x+b)(c x+d)

{\a}> {\c}

, then

\;{ {\b}+ {\d}}/{ {\a}+ {\c}}

is

a positive integer
a proper fraction
an improper fraction
a negative integer

Solution:

10 x^2+x-3

⇒ 10 x^2-5 x+6 x-3

⇒ 5 x(2 x-1)+3(2 x-1)

⇒(5 x+3)+(2 x-1)

By comparison:

(5 x+3)+(2 x-1)=(a x+b)(c x+d)

a=5

b=3

c=2

d=-1

Now,

\;{ {\b}+ {\d}}/{ {\a}+ {\c}}

⇒ \;{3-1}/{5+2}

⇒ \;{2}/{7}

∴ 2 \/ 7

is a proper fraction.
The correct option is 2 i.e. A proper fraction

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