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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

$open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0$

What is the product of the solutions to the given equation?

ExplanationShow

Choice D is correct. By the zero-product property, if $open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0$ , then $x minus 4, equals 0$ , $x plus 2, equals 0$ , or $x minus 1, equals 0$ . Solving each of these equations for $x$ yields $x equals 4$ , $x equals negative 2$ , or $x equals 1$ . The product of these solutions is $4 times negative 2, times 1, equals negative 8$ .

Choice A is incorrect and may result from sign errors made when solving the given equation. Choice B is incorrect and may result from finding the sum, not the product, of the solutions. Choice C is incorrect and may result from finding the sum, not the product, of the solutions in addition to making sign errors when solving the given equation.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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