Answer to Question #163467 in Algebra for Ava Brooke

Question

Use the rational root theorem to determine the list of all possible rational solutions.

y = 2 x 3 + 5 x 2 + 4

 

 

Answer 1

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