Q. 3 D5.0( 3 Votes )

Verify Whether the following are roots of the polynomial equations indicated against them.

x3 – 2x2 – x + 2 = 0; x = −1, 2, 3

Answer :

x3 – 2x2 – x + 2 = 0


p(x) = x3 – 2x2 – x + 2 = 0


p(-1) = (-1)3 – 2(-1)2 - (-1) + 2


= -1 – 2 × 1 + 1 + 2


= -1 – 2 + 1 + 2


= -3 + 3 = 0


x = -1 is a root of x3 – 2x2 – x + 2 = 0


p(x) = x3 – 2x2 – x + 2 = 0


p(2) = (2)3 – 2(2)2 – (2) + 2


= 8 – 2 × 4 – 2 + 2


= 8 – 8 – 2 + 2


= 10 – 10 = 0


x = 2 is a root of x3 – 2x2 – x + 2 = 0.


p(x) = x3 – 2x2 – x + 2 = 0


p(3) = (3)3 – 2(3)2 – (3) + 2


= 27 – 2 × 9 – 3 + 2


= 27 – 18 – 3 + 2


= 29 – 21 = 8 ≠ 0


x = 3 is not a root of x3 – 2x2 – x + 2 = 0.


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