Find a cubic function with the given zeros 6 2

Asked by admin @ 07/08/2021 in Math viewed by 311 People

Find a cubic function with the given zeros.
6, -3, 5

Answered by admin @ 07/08/2021

Answer:

f(x)=(x-6)(x+3)(x-5)= $x^3-8x^2-3x+90$ .

Explanation:

Multiply together linear factors with each of these zeros i.e 6 , -3 and 5.

f(x)=(x-6)(x+3)(x-5)

Expand first two roots:

$f(x)=(x^2-3x-18)(x-5)$

Expand further:

$f(x)=x^3-8x^2-3x+90$ .

Any polynomial in x with zeros(i.e 6 , -3, 5) will be a multiple (scalar or polynomial) of this f(x).

Therefore, the cubic function for the given zeros are: $f(x)=x^3-8x^2-3x+90$ .

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