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Degree of a Polynomial

Find all zero...

Question

Find all zeros of the polynomial 2x⁴ + 7x³ − 19x² − 14x + 30, if two of its zeros are $\sqrt{2} and - \sqrt{2}$ .

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Solution

We know that if is a zero of a polynomial, and then is a factor of .

Since and are zeros of .

Therefore

is a factor of . Now, we divide by to find the zero of .

By using division algorithm we have

Hence, the zeros of the given polynomial are .

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