x^3+13x=10x^2

Question

solve for all roots of the following polynomial functions.

Answer 1

The polynomial is x³ + 13x = 10x².

Rewrite the polynomail as x³ - 10x² + 13x  = 0.

Factor by grouping

Factor : x(x² - 10x + 13) = 0

Apply zero product property.

x = 0,  x² - 10x + 13 = 0

x² - 10x + 13 = 0 is quadratic, use the quadratic formula to find roots of the related quadratic equaton.

x = [ - b ± sqrt (b ^2 - 4ac )] / 2a.

Substitute b = - 10, a = 1, and c = 13.

x = [ - (- 10) ± sqrt ((- 10) ^2 - 4 * 1 * 13 )] / 2 *1

x = [ 10 ± sqrt (100 - 52)] / 2

x = [ 10 ± sqrt (48)] / 2

x = [ 10 ± 2 sqrt (12)] / 2

x = 5 ± sqrt (12)

x = 5 + 3.46, 5 - 3.46

x = 8.46, 1.54.

The roots of the polynomial are x = 0, x = 8.46, and x = 1.54.