Subjective Type

Solve the following equations: $$x^{3} - 15x^{2} - 33x + 847 = 0$$.

Solution

Given equation, $$x^3-15x^2-33x+847=0$$

$$\implies x^3 - 22x^2 + 7x^2 + 121x -154x + 847 = 0 \implies (x+7)(x^2-22x+121) = 0 \implies (x+7)(x-11)^2 = 0$$

$$\therefore\,\, x = -7,11,11$$

SIMILAR QUESTIONS

Theory of Equations

Solve the following equation: $$x^{3} - 18x = 35$$.

Theory of Equations

Solve the following equation: $$x^{3} + 72x - 1720 = 0$$.

Theory of Equations

Solve the following equation: $$x^{3} + 63x - 316 = 0$$.

Theory of Equations

Solve the following equation: $$x^{3} + 21x + 342 = 0$$.

Theory of Equations

Find the roots $$\alpha, \beta, \gamma$$ of $$x^{3}-11x^{2} +36x - 36 = 0$$ if $$\frac{2}{\beta} = \frac{1}{\alpha} + \frac{1}{\gamma}$$

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