Question

Find all the zeros of the polynomial (2x4 – 11x + 7x² + 13x – 7), it being
given that two of its zeros are (3 + V2) and (3 - 72).​

Answer 1

Step-by-step explanation:

The given polynomial is f(x) = 2x4 – 11x3 + 7x2 + 13x – 7.

Since (3 + √2) and (3 – √2) are the zeroes of f(x) it follows that each one of (x + 3 + √2) and (x + 3 – √2) is a factor of f(x).

Consequently, [(x – ( 3 + √2)] [(x – (3 – √2)] = [(x – 3) - √2 ] [(x – 3) + √2 ] = [(x – 3)2 – 2 ] = x2 – 6x + 7, which is a factor of f(x).

On dividing f(x) by (x2 – 6x + 7), we get:

Please see attachment after this

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