What is a polynomial function in standard form with zeros 1 2 3 and –3


Asked by maham237 @ in Mathematics viewed by 313 People

Answered by maham237 @



Answer:

f(x)=x^{4}-7x^{2}+3x^{3}-27x-18

Step-by-step explanation:

The polynomial function can be found by multiplying all roots. We know the four zeros, which we can express like this:

f(x)=(x+1)(x+2)(x+3)(x-3)

Now, we multiple to find the expression:

f(x)=(x^{2}+2x+x+2)(x^{2}-9)\\f(x)=x^{4}-9x^{2}+2x^{3}-18x+x^{3}-9x+2x^{2}-18\\f(x)=x^{4}-7x^{2}+3x^{3}-27x-18

Therefore the polynomial function with those four zeros is:

f(x)=x^{4}-7x^{2}+3x^{3}-27x-18


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