Question

obtain all the zeros of the polynomial FX equal to 2 x power 4 + x cube minus 14 x square - 19 x minus 6 if two of its zeros are - 2 and -1​

Answer 1

Hope it will help uhhh buddy .

Answer 2

$We \:have \: f(x) = 2x^{4}+x^{3}-14x^{2}-19x-6$

$-2 \: and \: -1 \: are \: zeroes \:of \: f(x)$

$(x+1)\:and \:(x+2) \:are \: factors \:f(x) .$

$So, (x+1)(x+2) = x^{2} + 3x + 2 \: is \:a \: factor \\of \: f(x)$

Quotient : 2x²-5x-3

x²+3x+2)2x⁴+x³-14x-19x-6

*********** 2x⁴+6x³+4x²

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*********** -5x³-18x²-19x

*********** -5x³-15x²-10x

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***************-3x²-9x-6

************** -3x²-9x-6

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Remainder (0)

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$Now , f(x) = (x+1)(x+2)(2x^{2}-5x-3) \\= (x+1)(x+2)(2x^{2}-6x+ 1x -3) \\= (x+1)(x+2)[2x(x-3)+1(x+3)] \\= (x+1)(x+2)(x-3)(2x+1)$

$(x-3) \:and \:(2x+1) \:are \:other \:two \: factors \\of \:f(x)$

$So, 3 \:and \:\frac{-1}{2} \:are \: other \:two \\zeroes \:of \:f(x)$

Therefore.,

$\green { 3 \:and \: \:\frac{-1}{2} \:are \: other}\\\green {two \:zeroes \:of \:f(x)}$

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