FIND A QUADRATIC POLYNOMIAL WHICH LEAVES A REMAINDER-2,-1,0 WHEN DIVIDED BY[X-1],[X+1] AND [X+2] RESPECTIVELY.

Asked by RAJDEEP NASKAR | 17th May, 2013, 06:56: PM

Expert Answer:

Let the quadratic polynomial f(x) = ax^2+bx+c
Hence, by remainder theorem
f(1) = -2 i.e a+b+c = -2 (1)
f(-1) = -1 i.e. a-b+c = -1 (2)
f(-2) = 0 i.e 4a-2b+c = 0 (3)

Subtracting equation 1 and 2
2b = -1
b = -1/2
Subtracting equation 2 and 3
3a-b = 1
3a = 1+(-1/2)
a = 1/6
 
Hence c = -2-a-b = -2-1/6+1/2 = -2 +1/3 = -5/3
 
So, the quadratic f(x) = 1/6x^2 -1/2x -5/3

Answered by  | 18th May, 2013, 05:34: AM

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