Math: 71014fb1

ID: 71014fb1

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: No work necessary.

Method 1: No real number, when squared, can equal a negative number, end of story. If there were something else after the squared value, such as a minus sign and some other number, then it might be a different story, but this problem requires no algebraic manipulation.

{real number}^2 ≠ -{real number}

The correct answer is (D).

Method 2: Use Desmos to graph the function and look for where the parabola intersects the x-axis.

You can see that there are no x-intercepts, so the correct answer is (D). The +4 shifts the graph up four units.

Method 3: Not that I would recommend doing so on the live exam, since there are simpler ways to approach the question, but you can work out the algebra and look to derive any solutions.

(x - 1)^2 + 4 = 0

(x^2 - 2x + 1) + 4 = 0

x^2 - 2x + 5 = 0

If there are any solutions, the discriminant of the quadratic formula, b^2 - 4ac, will have to be greater than or equal to 0.

(-2)^2 - 4(1)(5)

4 - 20 = -16

-16 < 0

The correct answer must be (D).