Question

Use the Quadratic Formula to solve 2x2 + 6x = –3. Which of the following gives the solutions to the nearest hundredth?

A. 2.37 and 0.63
B. 2.37 and –0.63
C. –2.37 and 0.63
D. –2.37 and –0.63

Answer 1

First, we need to put the equation in standard form, which is ax^2 + bx + c = 0. So, we have 2x^2 + 6x + 3 = 0.

Using the Quadratic Formula, x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can plug in the values for a, b, and c:

x = (-6 ± sqrt(6^2 - 4(2)(3))) / 2(2)

x = (-6 ± sqrt(36 - 24)) / 4

x = (-6 ± sqrt(12)) / 4

Simplifying further, we have:

x = (-6 ± 2sqrt(3)) / 4

x = (-3 ± sqrt(3)) / 2

To the nearest hundredth, the solutions are:

A. 2.37 and 0.63