Question

3x^3+x^2-55x+75=0

Answer 1

3 and 75 are two coefficients which give you clues to the zeros of this function
3 is possible root so try x=3
f(3) = 3(3)^3 + 3^2 - 55(3) + 75
= 81 + 9 - 165 + 75 = 0

so x=3 is one root

(possible roots are factors of 3*75)

others worth trying are 5 and -5

i'll try on my calculator
hold on a sec

Answer 2

ok -5 is also a root
so our expression

= (x + 5)(x - 3) (3x +/- a)

where a is the other root

as last term is + 75 it must be (3x - a)
-5*-3*-a = + 75
so a = 5

so we have (x-)(x+5)(3x-5) = 0

and 3 roots are 3, -5 and 5/3

Answer 3

sometimes if you can't only find one root you can use long division or synthetic division to get the other 2 roots