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Algebraic Identities

If x - 1 is a...

Question

If $(x - 1)$ is a factor of $a x^{3} - b x^{2} + c x$ , what is the value of $a^{3} - b^{3} + c^{3}$ ?

A

2abc

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B

-2abc

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C

3abc

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D

-3abc

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Solution

The correct option is D
-3abc

$p (x) = a x^{3} - b x^{2} + c x$

If (x - 1) is a factor then x = 1 is the zero of polynomial

p(1) = 0

$p (1) = a - b + c = 0$

It can be written as $a + (- b) + c = 0$

We know that if $a + b + c = 0, t h e n a^{3} + b^{3} + c^{3} = 3 a b c$

So, $a^{3} + {(- b)}^{3} + c^{3} = 3 a (- b) c = - 3 a b c$

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Similar questions

If $(x - 1)$ is a factor of $a x^{3} - b x^{2} + c x$ , what is the value of $a^{3} - b^{3} + c^{3}$ ?

x^{2} + x + 1

a x^{3} + b x^{2} + c x + d

, then real root of

a x^{3} + b x^{2} + c x + d = 0

(x - 1)^{3}

x^{4} + a x^{3} + b x^{2} + c x - 1

, then the other factor is

a x^{2} + b x + c = 0, b x^{2} + c x + a = 0

have common root

1

a, b, c

are zero real no. then find the value of

\frac{a^{3} + b^{3} + c^{3}}{3 a b c}

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root

a ≠ 0, then $\frac{a^{3} + b^{3} + c^{3}}{a b c} =$

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