$\"\"$

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The equation is $\"\"$ .

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Let $\"\"$ .

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Rational zeros method :

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Rational Root Theorem, if a rational number in simplest form $\"\"$ is a root of the polynomial equation $\"\"$ , then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor if_{$\"\"$ .}

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If $\"\"$ is a rational zero, then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor of $\"\"$ .

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The possible factors of $\"\"$ are $\"\"$ .

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The possible factors for $\"\"$ are $\"\"$ .

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So, $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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Using synthetic division:

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$\"\"$

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Since $\"\"$ , $\"\"$ is a zero of $\"\"$ .

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Therefore by factor theorem, $\"\"$ .

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The depressed polynomial of $\"\"$ is $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Using synthetic division:

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$\"\"$

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Since $\"\"$ , $\"\"$ is a zero of $\"\"$ .

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The depressed polynomial is $\"\"$ .

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Since the plynomial $\"\"$ has imaginary roots, the solutions of equation in real number system is $\"\"$ .

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$\"\"$

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The solutions of equation in real number system are $\"\"$ .