Use the rational root theorem to determine the list of all possible rational solutions.
y = 2 x 3 + 5 x 2 + 4
y = 2 x 3 + 5 x 2 + 4
According to the Rational Root Theorem, the zeroes for a rational number P/Q
P is the coefficient of independent term and Q is the coefficient of highest power term.
In this case, the Leading Coefficient is P = 2 (2x^3) and the Trailing Constant is Q = 4.
Therefore, the factor(s) are:
P = 2 = 1, 2
Q = 4 = 4, 2, 1
P Q P/Q F(P/Q)
-1 1 -1.00 7.00
-1 2 -0.50 5.00
-2 1 -2.00 8.00
-4 1 -4.00 -44.00
1 1 1.00 11.00
1 2 0.50 5.50
2 1 2.00 40.00
4 1 4.00 212.00
On solving the given polynomial, Followings are the roots:
There are one real root and two complex roots as given below:
Real Root: -2.76
Complex Root: 0.13 + 0.8 i and 0.13 - 0.8 i
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