Question

.If (x +2/3 ) is a factor of the polynomial p(x) = 3x^4 – 4x^3– ax + 2 then find the value of ‘a’?

Onlty right answers pls

Answer 1

$[tex] \pink{given : } \\ \\ (x + \frac{2}{3} ) \: \: is \: \: \: a \: \: \: factor \: \: \: of \: \: \: equation \\ \\ 3 {x}^{4} - 4 {x}^{3} - ax + 2 = 0 \\ \\ </p><p>\red{to \: \: \: find : } \\ \\ value \: \: \: of \: \: \: (\pink{a}</p><p>) \\ \\ \green{solution : } \\ \\ </p><p>\pink{put} \\ \\ x + \frac{2}{3} = 0 \\ \\ x = \frac{ - 2}{3} \\ \\ </p><p>\blue{put \: \: \: this \: \: \: value \: \: \: in \: \: \: \:main \: \: \: equation} \\ \\ 3(\pink{ { (\frac{ - 2}{3} })^{4} }</p><p>) - 4(\pink{ (\frac{ { - 2}^{3} }{ {3}^{3} } )}</p><p>) - a \times \pink{ \frac{ - 2}{3} } + 2 = 0</p><p></p><p> \\ \\ 3 \times \frac{16}{81} + 4 \times \frac{8}{27} + \frac{2a}{3} + 2 = 0 \\ \\ \frac{16}{27} + \frac{32}{27} </p><p> + \frac{2a}{3} + 2 = 0 \\ \\ \frac{16 + 32}{27} + \frac{2a}{3} + 2 = 0 \\ \\ \frac{48}{27} + \frac{2a}{3} + 2 = 0 \\ \\ \pink{multiply \: \: \: by \: \: \: 27}</p><p> \\ \\ \frac{48}{27} \times 27 + \frac{2a}{3} \times 27 + 2 \times 27 = 0 \\ \\ 48 + 2a \times 9 + 54 = 0 \\ \\ 18a + 102 = 0 \\ \\ 18a = - 102 \\ \\ a = \frac{ - 102}{18} \\ \\ a = \frac{ - 51}{9} \\ \\ a = \frac{ - 17}{3} \\ \\ \pink{hence} \\ \\ </p><p>\red{a =\blue{ \frac{ - 17}{3} }</p><p> }</p><p>$

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Answer 2

Answer:

here is your answer dear friend