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9: Find the equation of a polynomial with given zeros

9: Find the equation of a polynomial with given zeros-example-1

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Step-by-step explanation

We must find the equation of a polynomial with the following zeros: -5/4, -2/3 and 2.

(1) The general equation for this polynomial is:


f(x)=a\cdot(x-x_1)\cdot(x-x_2)\cdot(x-x_3).

Where x₁, x₂ and x₃ are the zeros.

(2) Replacing the zeros from above, we have:


f(x)=a\cdot(x+(5)/(4))\cdot(x+(2)/(3))\cdot(x-2).

(3) Expanding the last expression, we have:


f(x)=a\cdot(x^3-(1)/(12)x^2-3x-(5)/(3)).

(4) Comparing the last expression with the possibilities that we have as answers, we see that a = 12. Replacing this number in the expression above, we get:


f(x)=12x^3-x^2-36x-20.Answer

D.


f(x)=12x^3-x^2-36x-20.
User Aditay Kaushal
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