write polynomial

Question

write a polynomial f(x) of least degree in standard form that has rational coefficient, a leading coefficient of 1, and zeros 5 + √2 and -4

Answer 1

If 5 +√2 is a zero, then 5 - √2 should be also.

Then (x - (5 - √2))(x - (5 + √2))(x + 4)

(x² -(5 - √2)x - (5 + √2)x + (5 - √2)(5 + √2))(x + 4)

(x² -5x +√2x - 5x - √2x +25 - 5√2 + 5√2 - 2)(x+4)

(x² -10x +23)(x + 4)

(x² - 10x + 23)x + (x² - 10x + 23)4

x³ - 10x² + 23x +4x² - 40x + 92 =. x³ - 6x² - 17x + 92. should be a polynomial that works.

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