Question

Obtain all other zeros of x^4 5x^3 + 3x^2 + 15x - 18, if two of its zeros are √3 & -√3

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Answer 1

Answer:

x= $\sqrt{3}$, x=$-\sqrt{3}$

$(x-\sqrt{3})(x+\sqrt{3})$

=$(x)^{2} -(\sqrt{3})^2$

=$x^2-3$

$(x^4-5x^3+3x^2+15x-18)/x^2-3$

=$x^2-5x+6$

factorize $x^2-5x+6$

=$x^2-2x-3x+6$

=x(x-2)-3(x-2)

=(x-3)(x-2)

x=3, x=2

∴All four zeroes are 3, 2, $\sqrt{3}$ and $-\sqrt{3}$