Answer :
The solutions of the equation 3x^4 - 34x^3 + 128x^2 - 174x + 45 = 0 in the real number system are x = 1, x = 3, x = -3, and x = -5.
The equation can be solved using the Rational Root Theorem, which states that if the polynomial has a rational root, then the root must be of the form p/q, where p is a factor of the constant term 45 and q is a factor of the leading coefficient 3. The possible values of p are 1, 3, 5, 9, 15, and 45, and the possible values of q are 1, 3, and 9.
We can test each of the possible values of p/q to see if it is a root of the equation. The only values that work are p/q = 1/3, 3/3, -3/3, and -5/3. So, the solutions of the equation are x = 1, x = 3, x = -3, and x = -5.
The Rational Root Theorem can be used to solve any polynomial equation with rational coefficients. The theorem can also be used to find the possible values of the roots of a polynomial equation.
Learn more about Rational Root Theorem here: brainly.com/question/30098107
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Given question is incomplete, here is complete question:
Question. Solve the equation in the real number system.
3x4-34x3+128x2-174x+45=0
What are the real solutions of the equation? Select the correct choice below and, if necessary, fil in the answer box to complete your choice
OA The solution set is f
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type each answer only once)
B. The solution set is c
