Question

What are the zeros of the polynomial function: f(x) = x3 – 5x2 + 6x ?

Answer 1

Factor the equation:
\[f(x) = x^3-5x^2+6x = x(x^2-5x+6) = \]
(you should be able to factor the polynomial in the parentheses as well)
Remember that the zeros are the values of \(x\) such that \(f(x) = 0\) and because a polynomial can be written as the product of its factors, \[f(x) = 0 = x(x^2-5x+6)\]and\[x=0, x-r_1 = 0, x-r_2 = 0\) where \(r_1, r_2\) are the zeros of \(x^2-5x+6\)...

Answer 2

ackhthpth.

and \[x=0, x-r_1 = 0, x-r_2 = 0\]where \(r_1, r_2\) are the zeros of \(x^2-5x+6\)...

Answer 3

(x-3) (x-2) ?

Answer 4

@whpalmer4

Answer 5

yup so your factors are \(x\), \(x-2\), and \(x-3\)
now just set them all to zero and solve for x to find the zeros of the function :)

Answer 6

2,3,0 ?

Answer 7

yup :)

Answer 8

thanks man!

Answer 9

no problem!

Answer 10

yes, the full factoring of \[f(x) = x^3-5x^2+6x = x(x-2)(x-3)\]so the roots are found by solving \[x=0\]\[x-2=0\]\[x-3=0\] and are \[x = \{0,2,3\}\]