x^3+13x=10x^2

Question

solve for all roots of the following polynomial functions

Answer 1

x^3+13x=10x^2
solve for all roots of the following polynomial functions

x^3 + 13x = 10x^2
x^3 - 10x^2 + 13x = 0

Factor out an x.

x(x^2 - 10x + 13) = 0

Setting these factors equal to zero gives us our first root.

x = 0
x^2 - 10x + 13 = 0

Use the quadratic formula for the second expression.

      -b ± √(b² - 4*a*c)
x = --------------------
              2a

      -(-10) ± √((-10)² - 4*(1)*(13))
x = --------------------------------------
                   2(1)

      10 ± √(100 - 52)
x = ---------------------
                2

      10 ± √(48)
x = --------------
              2

      10 ± 6.9282
x = -----------------
              2

      10 + 6.9282                    10 - 6.9282
x = -----------------   and   x = -----------------
              2                                   2

      16.9282                    3.071797
x = -----------   and   x = --------------
            2                                2

x = 8.4641     and    x = 1.53589

There are three roots: x = 0, x = 8.4641, x = 1.53589