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