Question

obtain all zeroes of the polynomial 4x to the power of four + x cube - 72x square - 18x, if two zeroes are 3 root 2, -3 root 2

Answer 1

Answer:

Answer is 0 and -1/4 with this explaination hope you can understand well.

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Answer 2

Answer:

$\green { 0, \: \frac{-1}{4},3\sqrt{2} \:and}$ $\green {-3\sqrt{2}\:are \: zeroes \:of \:p(x) }$

Step-by-step explanation:

$Given \: 3\sqrt{2}, \:and \:-3\sqrt{2} \:are \: two\\zeroes \: of \: the \:polynomial \\ p(x) = 4x^{4}+x^{3}-72x^{2} -18x \\= x(4x^{3}+x^{2}-72x-18)$

$(x-3\sqrt{2})(x+3\sqrt{2}) \\= x^{2} - (3\sqrt{2})^{2}\\= x^{2} - 18 \: is \:a \: factor \: of \: p(x)$

x²-18) 4x³+x²-72x-18 ( 4x+1

******* 4x³ + 0 -72x

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*********** x² - 18

*********** x² - 18

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Remainder (0)

p(x) = x(x²-18)(4x+1)

$Other \: two \: zeroes \: are \: x = 0 \:Or \: 4x+1 = 0$

$x = 0 \:Or \: x = \frac{-1}{4}$

Therefore.,

$\green { 0, \: \frac{-1}{4},3\sqrt{2} \:and}$ $\green {-3\sqrt{2}\:are \: zeroes \:of \:p(x) }$

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