Find all the zeros of the polynomial $2 x^{3} + x^{2} - 6 x - 3,$ if two of its zeros are $- \sqrt{3}$ and $\sqrt{3}$ .

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Solution

Sum of zeroes = $fraction numerator negative space left parenthesis space c o e f f i c i e n t space o f space x Â² right parenthesis over denominator left parenthesis c o e f f i c i e n t space o f space x Â³ right parenthesis end fraction$
Let the third root be x,
then
x + - = $fraction numerator negative 1 over denominator 2 end fraction$
x = $fraction numerator negative 1 over denominator 2 end fraction$

So, the third root is $fraction numerator negative 1 over denominator 2 end fraction$

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Similar questions

- \sqrt{3} and \sqrt{3}

Find all zeroes of the polynomial $2 x^{3} + x^{2} - 6 x - 3$ if two of its zeroes are $- \sqrt{3}$ & $\sqrt{3}$

f (x) = 2 x^{4} - 2 x^{3} - 7 x^{2} + 3 x + 6

- \sqrt{\frac{3}{2}}

\sqrt{\frac{3}{2}}

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