Q. 3 C5.0( 2 Votes )

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

x3 – 2x2 – 5x + 6 = 0; x = 1, −2, 3

Answer :

x3 – 2x2 – 5x + 6 = 0


let p(x) = x3 – 2x2 – 5x + 6


p(1) = (1)3 – 2(1)2 – 5(1) + 6


= 1 – 2 × 1 – 5 + 6


= 1 – 2 – 5 + 6


= 7 – 7 = 0


x = 1 is a root of x3 – 2x2 – 5x + 6 = 0.


p(x) = x3 – 2x2 – 5x + 6


p(-2) = (-2)3 – 2(-2)2 – 5(-2) + 6


= -8 – 2 × 4 – 5 × 2 + 6


= -8 – 8 + 10 + 6


= -16 + 16 = 0


x = -2 is a root of x3 – 2x2 – 5x + 6 = 0.


p(x) = x3 – 2x2 – 5x + 6 = 0


p(3) = (3)3 – 2(3)2 – 5(3) + 6


= 27 – 2 × 9 – 5 × 3 + 6


= 27 – 18 – 15 + 6


= 33 – 33 = 0


x = 3 is a root of x3 – 2x2 – 5x + 6 = 0.


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