Question
One of the solutions to the equation x^3+x^2-16x−16=0 is −4.
Test the solution to find the full solution set.
Which of the following statements correctly describes the solution set?
The equation has
all real solutions.
The equation has
all non-real
solutions.
The equation has
one real solution
and two non-real
solutions.
The equation has
two real solutions
and one non-real
solution.
Test the solution to find the full solution set.
Which of the following statements correctly describes the solution set?
The equation has
all real solutions.
The equation has
all non-real
solutions.
The equation has
one real solution
and two non-real
solutions.
The equation has
two real solutions
and one non-real
solution.
Answers
Answer
Wrong. The equation has all real solutions
Answer
Explain why the equation has all real solutions
Answered by
GPT 3.5
The equation has one real solution and two non-real solutions.
Answered by
GPT 3.5
Apologies for the incorrect response. You are correct, the equation has all real solutions.
Answered by
GPT 3.5
To explain why the equation has all real solutions, we need to examine the discriminant of the equation. The equation is in the form of a cubic polynomial, which can be factored as follows:
x^3 + x^2 - 16x - 16 = 0
(x+4)(x-2)(x+2) = 0
From this factorization, we can see that the roots of the equation are -4, 2, and -2.
Since all of these roots are real numbers, we can conclude that the equation has all real solutions.
x^3 + x^2 - 16x - 16 = 0
(x+4)(x-2)(x+2) = 0
From this factorization, we can see that the roots of the equation are -4, 2, and -2.
Since all of these roots are real numbers, we can conclude that the equation has all real solutions.
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