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2.2 Nonlinear Equations in One Variable - Quadratic solving (factoring, quadratic formula, completing square)

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$x squared, minus x, minus 1, equals 0$

What values satisfy the equation above?

A.

$x equals 1$ and $x equals 2$

B.

$x equals negative one half$ and $x equals three halves$

C.

$x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2$ and $x equals, the fraction with numerator 1 minus the square root of 5, and denominator 2$

D.

$x equals, the fraction with numerator negative 1 plus the square root of 5, and denominator 2$ and $x equals, the fraction with numerator negative 1 minus the square root of 5, and denominator 2$

What values satisfy the equation above?

Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice C is correct. Using the quadratic formula to solve the given expression yields $x equals, the fraction with numerator negative, open parenthesis, negative 1, close parenthesis, plus or minus, the square root of open parenthesis, negative 1, close parenthesis, squared, minus, 4 times 1 times negative 1, end root, and denominator, 2 times 1, end fraction, which equals, the fraction with numerator 1, plus or minus, the square root of 5, and denominator 2$ . Therefore, $x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2$ and $x equals, the fraction with numerator 1 minus the square root of 5, and denominator 2$ satisfy the given equation.

Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic formula. Choice D is incorrect and may result from a sign error.

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