Question

9: Find the equation of a polynomial with given zeros

Answer 1

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.`