AP ICET 2019 Shift 2 Paper

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Question : 125 of 200

Marks: +1, -0

If

ax^4+bx^3+2x^2+4

is exactly divisible by

x^2-x-2

, then (a, b) =

$(1/2, -3/2)$
$(3/2,5/2)$
$(5/2,7/2)$
$(-5/2,7/2)$

Solution:

Let

f(x)=a x^{4}+b x^{3}+2 x^{2}+4

x^{2}-x-2 ⇒(x-2)(x+1)

∴f(2)=0 ⇒ 16 a+8 b+12=0

→ (1)

f(-1)=0 ⇒ a-b+6=0

→ (2)
solving (1)&(2)

({-5}/2,7/2)

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