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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.

6 x squared, plus 5 x, minus 7, equals 0

What are the solutions to the given equation?

ExplanationShow

Choice A is correct. The quadratic formula, x equals, the fraction with numerator negative b plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction, can be used to find the solutions to an equation in the form a, x squared, plus b x, plus c, equals 0. In the given equation, a, equals 6, b equals 5, and c equals negative 7. Substituting these values into the quadratic formula gives the fraction with numerator negative 5 plus or minus, the square root of, 5 squared minus 4, times 6, times 7, end root, and denominator 2 times 6, end fraction, or the fraction with numerator negative 5 plus or minus, the square root of, 25 minus 168, end root, and denominator 12, end fraction.

Choice B is incorrect and may result from using the fraction with numerator negative a, plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction as the quadratic formula. Choice C is incorrect and may result from usingthe fraction with numerator negative b plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction as the quadratic formula. Choice D is incorrect and may result from using the fraction with numerator negative a, plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction as the quadratic formula.

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