Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

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Solution

$p (x) = 3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$

Since the two zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ ,

$∴ (x - \sqrt{\frac{5}{3}}) (x + \sqrt{\frac{5}{3}}) = (x^{2} - \frac{5}{3}) i s a f a c t o r o f 3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ .

Therefore, we divide the given polynomial by $x^{2} - \frac{5}{3}$ .

We factorize $3 x^{2} + 6 x + 3 = 0$
$= 3 (x^{2} + 2 x + 1) = 0$

$= (x + 1)^{2} = 0$

Therefore, its zero is given by x + 1 = 0.

x = -1

As it has the term $(x + 1)^{2}$ , therefore, there will be 2 zeroes at x = - 1.

Hence, the zeroes of the given polynomial are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ and – 1.

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Similar questions

Q. Obtain all other zeroes of

3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5

, if two of its zeroes are

\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}

Q. Obtain all the other zeros of

3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5.

if two of its zeros are

\sqrt{\frac{5}{3}} and - \sqrt{\frac{5}{3}} .

Question 3
Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Question 3
Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Q. Obtain all the zeroes of

3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5

, if of its zeroes are

\sqrt{\frac{5}{3}}

- \sqrt{\frac{5}{3}}

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Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .