Question

Write the equation of a cubic function f(x) that has zeros x = –3, x = –1 and x = 2.

Answer 1

Consider that the cubic function having zeroes a, b, c, is given by,

`f(x)=x^3-(a+b+c)x^2+(ab+bc+ac)-abc`

Given that the zeroes of the cubic function are -3, -1, and 2,

`\begin{gathered} a=-3 \\ b=-1 \\ c=2 \end{gathered}`

Substitute the values to obtain the cubic function,

`\begin{gathered} f(x)=x^3-\mleft\lbrace\mleft(-3\mright)+\mleft(-1\mright)+2\mright\rbrace x^2+\mleft\lbrace\mleft(-3\mright)\mleft(-1\mright)+\mleft(-1\mright)2+\mleft(-3\mright)2\mright\rbrace-(-3)(-1)2 \\ f(x)=x^3-\mleft\lbrace-3-1+2\mright\rbrace^{}x^2+\mleft\lbrace3-2-6\mright\rbrace x-6 \\ f(x)=x^3-(-2)x^2+(-5)x-6 \\ f(x)=x^3+2x^2-5x-6 \end{gathered}`

Thus, the required cubic function is obtained as,

`f(x)=x^3+2x^2-5x-6`