Question

find all the zeros of the polynomial 5 x cube minus 15 x square - 3 x + 9 if two of its zeros are whole root 3 upon 5 and minus 4 root 3 upon 5​

Answer 1

$Let \: p(x) = 5x^{3} - 15x^{2} - 3x + 9$

$\sqrt{\frac{3}{5}} \:and \: -\sqrt{\frac{3}{5}}\:are \\two \: zeroes \: of \: p(x)$

$\left( x - \sqrt{\frac{3}{5}}\right) \left( x + \sqrt{\frac{3}{5}}\right) \\= x^{2} - \left( \sqrt{\frac{3}{5}}\right)^{2} \\= x^{2} - \frac{3}{5}\\= \frac{5x^{2} - 3}{5} \\= \frac{1}{5} ( 5x^{2} - 3) \: is \: a \: factor \: p(x)$

5x²-3| 5x³-15x² - 3x + 9 | x-3

******** 5x³ + 0 - 3x

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************** -15x² + 0 + 9

************** -15x² + 0 + 9

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Remainder (0)

(x-3) is a factor of p(x)

Therefore.,

$3 \: is \: other \: zero \: of \: p(x)$

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Answer 2

Answer:

Try to do it by yourself