Verify whether the following are roots of the polynomial equations indicated against them.
$x^{3} + 8 x^{2} + 5 x - 14 = 0; x = 1, 2$

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Solution

Let $p (x) = x^{3} + 8 x^{2} + 5 x - 14$
$p (1) = (1)^{3} + 8 (1)^{2} + 5 (1) - 14 = 1 + 8 + 5 - 14 = 0$
x=1 is root of $x^{3} + 8 x^{2} + 5 x - 14 = 0$
But $p (2) = (2)^{3} + 8 (2)^{2} + 5 (2) - 14 = 8 + 32 + 10 - 14 = 36 \neq 0$
x=2 is root of $x^{3} + 8 x^{2} + 5 x - 14 = 0$

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