Mathematics: Find a cubic function with the given zeros. square root of 6, - square root of 6, -3

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Find a cubic function with the given zeros. square

srshelton

31.12.2021

$x^{3} +3x^{2} -6x-18$

Step-by-step explanation:

We are given zeroes and we need to find a cubic function with these zeroes

zeroes given are : $\sqrt{6} , - \sqrt{6} , -3$

Since these are zeroes so these can be written as:

$(x-\sqrt{6} )(x-(-\sqrt{6} ))(x-(-3)) = 0$

⇒ $(x-\sqrt{6} )(x+\sqrt{6} )(x+3) = 0$

⇒ $(x^{2} +\sqrt{6} x- \sqrt{6} x -6)(x+3)$

⇒ $(x^{2} -6)(x+3)$

⇒ $x^{3} +3x^{2} -6x-18$

Thus the required cubic function is $x^{3} +3x^{2} -6x-18$

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