6x^3 +5x^2 −6x−5=0


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Question Number 58092 by smiak8742 last updated on 17/Apr/19

$6 x^{3} + 5 x^{2} - 6 x - 5 = 0$
	Answered by tanmay last updated on 17/Apr/19

	$6 x^{3} - 6 x + 5 x^{2} - 5 = 0$ $6 x (x^{2} - 1) + 5 (x^{2} - 1) = 0$ $(x^{2} - 1) (6 x + 5) = 0$ $(x + 1) (x - 1) (6 x + 5) = 0$ $x = - 1, 1 a n d \frac{- 5}{6}$
	Answered by Kunal12588 last updated on 17/Apr/19

	$6 x^{3} + 5 x^{2} - 6 x - 5 = 0$ $\Rightarrow x^{2} (6 x + 5) - 1 (6 x + 5) = 0$ $\Rightarrow (x^{2} - 1) (6 x + 5) = 0$ $\Rightarrow (x - 1) (x + 1) (6 x + 5) = 0$ $\Rightarrow x = 1 o r x = - 1 o r x = - \frac{5}{6}$
	Answered by MJS last updated on 17/Apr/19

	$first try all factors of 5 :$ $x = - 5 \Rightarrow no solution$ $x = - 1 \Rightarrow solution x_{1} = - 1$ $x = 1 \Rightarrow solution x_{2} = 1$ $x = 5 \Rightarrow no solution$ $6 (x + 1) (x - 1) (x - x_{3}) = . . . - 5$ $6 \times 1 \times (- 1) \times (- x_{3}) = - 5$ $6 x_{3} = - 5$ $x_{3} = - \frac{5}{6}$
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