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Factor Theorem

Obtain all ze...

Question

Obtain all zeros of the polynomial f(x) = 2x⁴ + x³ − 14x² − 19x − 6, if two of its zeros are −2 and −1.

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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 other zeros of .

By using division algorithm we have,

Hence, the zeros of the given polynomials are.

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