Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 - 5$ $i f t w o i t s z e r o s a r e \sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$

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Polynomial $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 - 5$ $i f t w o i t s z e r o s a r e \sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ $x = \sqrt{\frac{5}{3}} a n d x = - \sqrt{\frac{5}{3}} (x + \sqrt{\frac{5}{3}}) (x - \sqrt{\frac{5}{3}}) = x^{2} - \frac{5}{3} \Rightarrow 3 x^{2} - 5$
$∴ 3 x^{2} + 6 x^{3} - 2 x^{2} - 10 x - 5$ Apply division algorithm to the polynomial and $3 x^{2} - 53 x^{2} + 0 - 5 x^{2}$
- +...........................
$6 x^{3} + 3 x^{2} - 10 x - 5$ $6 x^{3} + 0 - 10 x$
- + ..............
$6 x^{3} + 3 x^{2} - 10 x - 5$ $6 x^{3} + 0 - 10 x$ First term of quotient is $\frac{3 x^{4}}{3 x^{2}} = x^{2}$
Second term of quotient is
$\frac{6 x^{3}}{3 x^{2}} = 2 x$
Third term of quotient is $\frac{3 x^{2}}{3 x^{2}} = 1$ $∴ 3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5 = (3 x^{2} - 5) (x^{2} + 2 x + 1) + 0$ $∴ Q u o t i e n t = x^{2} + 2 x + 1 = (x + 1)^{2} ∴ x = - 1 a n d - 1$ $∴∴ Z e r o e s o f (x + 1)^{2} a r e - 1, - 1 \sqrt{\frac{5}{3}} a n d \sqrt{\frac{5}{3}}$

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Q. Obtain all the other zeros of

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if two of its zeros are

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Question 3
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Obtain all other zeroes of3x4+6x3−2x2−10−5 iftwoitszerosare√53and−√53

Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 - 5$ $i f t w o i t s z e r o s a r e \sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$