Question

Plz answer to this..


Given that x-√5 is a factor of the cubic polynomial x^-3√5+13x-3√5, find all the zeros of the polynomial.

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Answer 1

given that x-√5 is a factor of the cubic polynomial x3-3√5x2+13x-3√5

x-√5 ) x3-3√5x2+13x-3√5 ( x2 -2√5x + 3

x3- √5x2 ( substract )

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- 2√5x2+13x

- 2√5x2+10x ( substract )

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3x - 3√5

3x - 3√5 ( substract )

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0

∴ The quotient is x2 -2√5x + 3 = 0

Using roots of quadratic formula

a = 1, b = 2√5, c = 3

x = (-b ± √(b2 - 4ac) ) / 2a

x = (2√5 ± √((2√5)2 - 12) ) / 2

∴ the other zeros are x = √5 ± √2.

Hope it helps you!