Question

The function $f\left(x\right)$ intersects the x-axis at $x=-5,x=2$, and $x=4$. If the equation of $f\left(x\right)$ can be written in the form $y=a{x}^3+b{x}^2+cx+d$, with $a=1$, choose the possible equation representing $f\left(x\right)$.

• A. $y=x^3-x^2-38x-40$
• B. $y=x^3+x^2-22x-40$
• C. $y=x^3-x^2-22x+40$
• D. $y=x^3+5x^2+8x+40$

Answer 1

Answer: (C)

$y=x^3-x^2-22x+40$

Substitute the value of x in the equation $y=x^3-x^2-22x+40$
We get the value of y = 0, then that is the possible equation.
When x = -5, $y=(-5{)}^3-(-5{)}^2-22(-4)+40=0$
x = 2, $y=(2{)}^3-(2{)}^2-22\left(2\right)+40=0$
x = 4, $y=(4{)}^3-(4{)}^2-22\left(4\right)+40=0$
So, the possible equation is $y=(2{)}^3-(2{)}^2-22\left(2\right)+40=0$.