Which of the following are roots of the polynomial function? (check all that apply) f(x)=x^3-7x^2+13x-6

the answers is b,d, and f

Step-by-step explanation:

B, D and F

Step-by-step explanation:

Roots are the x intercepts of a curve i.e the points where the curve crosses or touches the x axis. Since these are always on the x axis, the y coordinates of these points are always 0. So to find the answer here, you substitute each possible answer into the function and it if it gives you y=0 then you know that it is a root. (2,0) being the first example.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb