Determine the equation whose roots are - 1 - 5 and - 3

Well you are given the roots.

if we have 3 it would. have to be x^3. So something like:

y = ax^3 + bx^2 + cx + d

this could. also be written:

y = (x + a) (x + b) (x + c)

when you are able to write it like this, we know that the opposite of a, b, and c are roots. this is because if we can make any of the insides of the 3 parenthesis equal 0 then y = 0 and that x. is a root. Well if we know the 3 roots that x will be then we just have to figure out the a, b, and c. So let's plug our roots in.

y = (-1 + a) (-5 + b) (-3 + c)

now we have to make each parenthesis equal 0 to find what a, b, and c should be. It is obvious a = 1 to make. that one zero and b = 5 and c = 3. So we know a, b, and c. now let's plug. those into our first equation.

y = (x + 1) (x + 5) (x + 3)

this is your equation. You can multiply out if necessary