Question

What are the roots of the polynomial equation x^3-6x= 3x^2-8? Use a graphing calculator and a system of equations.
–40, –4, 5
–5, 4, 40
–4, –1, 2
–2, 1, 4

Answer 1

Given the polynomial equation x^3 -6x = 3x^2 – 8. Which can be simplified into (x^3) -3(x^2) -6x +8 = 0. The roots of the given equation are x = -2, x = 1 and x = 4. The order  of equation also represents the number of roots of the equation given. Since the highest exponent is 3, there also 3 roots. So the answer is D. 2 –2, 1, 4  

 

Answer 2

x^3 -6x = 3x^2 -8

x^3 - 3x^2 -6x = -8

x^3 - 3x^2 -6x +8 = 0

 now factor:

(x-4) (x^2+x-2) = 0

(x-4) (x-1)(x+2) = 0

 the roots are  4, 1, -2

 answer is the last one