What is the positive solution to the equation x^2 - 3x - 28 =... | SAT Nonlinear equations in one variable and systems of equations in two variables Question, Answer Explained

Math · Advanced MathEasy

What is the positive solution to the equation $x^2 - 3x - 28 = 0$ ?

$3$

$4$

$7$

$28$

Show answer and explanation

Answer: C

Factor: $(x - 7)(x + 4) = 0$ . So $x = 7$ or $x = -4$ . The positive solution is $7$ .

Choice B reverses the signs when factoring. Substituting $4$ gives $16 - 12 - 28 = -24$ , not $0$ .

Why the other choices are wrong

A. 3 is the sum of the solutions, 7 + (-4), not a solution itself.
B. The factors are (x - 7)(x + 4), so the solutions are 7 and -4. Substituting 4 gives -24, not 0.
D. Substituting 28 gives 784 - 84 - 28 = 672, not 0. The constant term is the product of the solutions.

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