Question

find the roots of the polynomial equation 2x^3+2x^2-19x+20=0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the roots of the polynomial equation 2x^3 + 2x^2 - 19x + 20 = 0, we can use various methods such as factoring, synthetic division, or numerical methods.

One method to find the roots is factoring by grouping.

2x^3 + 2x^2 - 19x + 20 = 0

Rearranging the terms:

2x^3 - 19x + 2x^2 + 20 = 0

Grouping the terms:

(x^2 + 10)(2x - 1) = 0

Setting each factor equal to zero:

x^2 + 10 = 0 OR 2x - 1 = 0

Solving the first equation:

x^2 + 10 = 0
x^2 = -10
x = ± √(-10)

Since there is no real number that satisfies the equation x^2 = -10, this quadratic factor does not have real solutions.

Solving the second equation:

2x - 1 = 0
2x = 1
x = 1/2

Therefore, the only real root of the polynomial equation 2x^3 + 2x^2 - 19x + 20 = 0 is x = 1/2.