Quadratic Formula with Complex Solutions Warmup 2

Solve -2x² + 4x = 9

• (2 - i√14)/2   ,   (2 + i√14)/2

• (2 - i√-56)/2   ,   (2 + i√-56)/2

• (2 - i√-14)/2   ,   (2 + i√-14)/2

• (2 - √14)/2   ,   (2 + √14)/2

Answer explanation

To solve -2x² + 4x = 9, rearrange to -2x² + 4x - 9 = 0. Using the quadratic formula, the roots are (2 ± i√14)/2. Thus, the correct answers are (2 - i√14)/2 and (2 + i√14)/2.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Factor

• Write down: a = 1, b = 6, c = -13

• Subtract 3 from both sides.

• Add 3 to both sides.

Answer explanation

To solve the equation x² + 6x - 13 = 3, the first step is to isolate the quadratic expression. Subtracting 3 from both sides gives x² + 6x - 16 = 0, which is necessary for further solving.

Tags

CCSS.HSA-REI.B.4B

Which of the following has imaginary solutions?

Answer explanation

The equation 5x^2 - 2x + 6 = 0 has a negative discriminant (b^2 - 4ac = (-2)^2 - 4*5*6 < 0), indicating it has imaginary solutions. The other equations have non-negative discriminants.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Answer explanation

To solve the equation 2x^2 + 4x + 10 = 0, we use the quadratic formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a = 2, b = 4, c = 10. The discriminant (b^2 - 4ac) is negative, leading to complex solutions: -1 \pm 2i.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Answer explanation

The correct choice is the third one, which properly applies the quadratic formula. It uses -6 for the coefficient of x, includes the correct discriminant calculation with -16, and formats the equation correctly.

Tags

CCSS.HSA-REI.B.4B

What are the zeros of the function f(x) = x² + 64?

• -8 and 8

• -8i and 8i

• (-√8) i and (√8) i

• -√8  and √8

Answer explanation

The function f(x) = x² + 64 has no real zeros since it is always positive. To find the zeros, set f(x) = 0, leading to x² = -64. The solutions are x = ±8i, making the correct answer -8i and 8i.