Find all rational zeros of f. Then (if necessary) use the depressed equation to find all roots of the equation
f(x)equals=0.
f(x)= 5x^3-x^2-15x+3
set of all zeros of the given function is= ___ OR NO REAL ZEROS
Using the rational root theorem, try these values for a possible solution: 1, -1, 3, -3, 1/5, -1/5, 3/5, -3/5
Trying these, you can find that 1/5 is a solution.
This means that (5x - 1) is a factor.
Divide 5x3 - x2 - 15x + 3 by 5x -1 ---> the quotient is x2 - 3
Solving x2 - 3 = 0
---> x = +/-sqrt(3)
Using the rational root theorem, try these values for a possible solution: 1, -1, 3, -3, 1/5, -1/5, 3/5, -3/5
Trying these, you can find that 1/5 is a solution.
This means that (5x - 1) is a factor.
Divide 5x3 - x2 - 15x + 3 by 5x -1 ---> the quotient is x2 - 3
Solving x2 - 3 = 0
---> x = +/-sqrt(3)