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The number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
In order to determine the number of solutions, we would split the single equation to two different equations and then plot a graph, so as to reveal their solutions.
This ultimately implies that, the number of solutions is equal to the point of intersection between the lines of the equations plotted on a graph.
In conclusion, the number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
Read more on number of solutions here: brainly.com/question/12558210
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Answer:
Step-by-step explanation:
We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure , where <u>p is any of the factors of the constant term and q is any of the factors of the leading coefficient</u>.
In this example, -15 is the constant term and 1 is the leading coefficient ( has a coefficient of 1).
The factors of -15 are , while the factors of 1 are
. <em>p </em>is can be any one of the factors of -15, while <em>q</em> can be any of the factors of 1.
The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are .