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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 the rational root theorem.
By testing various factors of the constant term 20 (±1, ±2, ±4, ±5, ±10, ±20) divided by the factors of the leading coefficient 2 (±1, ±2), we can find the possible rational roots.
By trying these potential rational roots, we can find the one root of the equation: x = -1.
Performing polynomial division by (x + 1), we can reduce the equation to (x^2 + x - 20) = 0.
Factoring this quadratic equation, we get (x + 5)(x - 4) = 0.
Setting each factor equal to zero, we find the remaining roots:
x + 5 = 0 → x = -5
x - 4 = 0 → x = 4
Therefore, the roots of the polynomial equation 2x^3 + 2x^2 - 19x + 20 = 0 are -5, -1, and 4.