TS ICET 23 May 2018 Shift 1 Paper

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Question : 124 of 200

Marks: +1, -0

If

x^2-3x+2

is a factor of

x^3-6x^2+ax+b.

then (a. b) = ?

(-11, -6)
(11.6)
(-11, 6)
(11, -6)

Solution:

x^2 – 3x + 2 = (x -1)(x-2)

Let

f(x)=x^3-6x^2+ax+b

Given

x^2-3x+2

is a factor of f(x)
⇒f(1) = 0 and f(2) = 0
If

f(1)=0⇒(1)^{3}-6(1)^{2}+a(1)+b=0

⇒ a+b=5

→(1)
If

f(2)=0 ⇒(2)^{3}-6(2)^{2}+a(2)+b=0

⇒2a + b = 16

→ (2)
From (1) and (2) we get, a = 11 and b = – 6

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