Given equation $x^{6}$ - $x^{5}$ + $x^{4}$ - $x^{3}$ + $x^{2}$ - x + 1 = 0 can also be written as _________.

where 1 + x ≠ 0

1 + = 0

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1 + x = 0

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1 + = 0

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1 + = 0

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Solution

The correct option is C
1 + = 0

Given 1 - x + $x^{2}$ - $x^{3}$ + $x^{4}$ - $x^{5}$ + $x^{6}$ = 0

we see that given series is a GP with common ratio (-x)

Sum of the GP

$\frac{1 (1 - (- x)^{7})}{1 - (- x)}$ = 0 where 1 + x $\neq 0$

1 + $x^{7}$ = 0

Suggest Corrections

Similar questions

Fill all the roots of the equation.

$x^{6}$ - $x^{5}$ + $x^{4}$ - $x^{3}$ + $x^{2}$ - x + 1 = 0 1 + x $\neq 0$

x \neq - 1

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1} = 1

\frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}

\frac{x}{6}

\frac{x}{6}

α, β, γ, δ

x^{4} - x^{3} - x^{2} - 1 = 0.

p (x) = x^{6} - x^{5} - x^{3} - x^{2} - x,

p (α) + p (β) + p (γ) + p (δ)

x^{6} - x^{5} + x^{4} - x^{2} + x - 1 = 0

x ϵ 0

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