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 = 0, we rearrange to 2x² - 4x + 9 = 0. Using the quadratic formula, we find 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

Answer explanation

Using the quadratic formula \( q = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), we identify \( a = -12, b = 3, c = 7 \). Calculating the discriminant gives \( \sqrt{345} \), leading to the solution \( \frac{3 \pm \sqrt{345}}{24} \).

Tags

CCSS.HSA-REI.B.4B

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 before factoring or using the quadratic formula.

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

In the equation x^2 + 8x - 3 = 0, the standard form is ax^2 + bx + c. Here, a = 1 (coefficient of x^2), b = 8 (coefficient of x), and c = -3 (constant term). Thus, the correct values are a=1, b=8, c=-3.

Answer explanation

The correct choice is the third one, which properly applies the quadratic formula. It uses -6 for the coefficient of x, and correctly calculates the discriminant with -16, ensuring the signs and values are accurate.

Tags

CCSS.HSA-REI.B.4B