TS ICET 24 May 2019 Shift 1 Paper

Question : 125 of 200

Marks: +1, -0

If a polynomial in x leaves remainders -19, 17 respectively when divided by x + 4 and x - 5. then the remainder it leaves when divided by

x^2 - x-20

Solution:

Let the remainder be ax + b and quotient be Q(x) then by divisible algorithm.

f(x)=(x^{2}-x-20)(2(x)+a x+b

Given

f(–4) = –19 ; f(5) = 17

-19 =-4a + b

→ (1)

17 = 5a + b

→ (2)
Solving (1) and (2)

a = 4, b = –3

∴ Remainder

=4x-3

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