Find all zeros of the polynomial fx-2 x4-2 x3-7 x2-3 x-6- if its two zeros are -32 and 32 -

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Standard X

Mathematics

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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Find all zeros of the polynomial f(x) = 2x4 − 2x3 − 7x2 + 3x + 6, if its two zeros are -32 and 32.

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 .

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

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 .