Question

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Obtain all the zeroes of 3x^4+ 6x^3-2x^2-10x-5, if two of its zeroes are root 5/3 and -root 5/3.

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Answer 1

Heya,

here is your answer,

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$it \: is \: given \: that \: \sqrt{ \frac{5}{3} } \: and \: - \sqrt{ \frac{5}{3} } \: are \: two \: zeros \: of \: f(x). \: therefore \: \\ \\ (x - \sqrt{ \frac{5}{3} } ) \: (x + \sqrt{ \frac{5}{3} } \: is \: a \: factor \: of \: f(x). \: but \: (x - \sqrt{ \frac{5}{3} } )(x + \sqrt{ \frac{5}{3} }) = \frac{1}{3} (3 {x}^{2} - 5) \\ \\ therefore \: \: 3 {x}^{2} - 5 \: is \: a \: factor \: of \: f(x). \: let \: us \: now \: divide \: f(x) \: by \: 3 {x}^{2} - 5 \\ \\ using \: long \: division \: method \: . \: we \: obtain \: \\ \\ (now \: refer \: pic \: )$

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Hope this helps you ☺☺

# Nikky

Best wishes :))