In the given equation, $c$ is a constant. For which of the following values of $c$ will the equation have more than two real solutions?
$$x^2(x+1)+4x(x+1)+c(x+1)=0$$
Answer:
A
Explanation
The correct answer is Choice A.
Factor the given equation to determine the number of $x$-intercepts, to find the value of $c$ such that the given equation has more than two solutions.
Therefore, $c=2$ is the only value from the given choices for the equation to have more than two solutions.Choice B is incorrect and may result from finding a value that gives exactly two real solutions.
Choices C and D are incorrect and may result from algebraic mistakes.
✨ Expert's Tip ✨
When factored into a perfect squared, the solution derived from the factor only counts as one real solution.