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Factor Theorem

Find all zero...

Question

Find all zeros of the polynomial f(x) = 2x⁴ − 2x³ − 7x² + 3x + 6, if its two zeros are $- \sqrt{\frac{3}{2}} and \sqrt{\frac{3}{2}}$ .

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Solution

Since and are two zeros of .Therefore,

is a factor of .

Also is a factor of .

Let us now divide by. We have,

By using division algorithm we have,

Hence, The zeros of are .

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