Can you explain how to find the solution of 3x^2-2x+5, using the quadratic formula? I got it down to (2 +/- sq. root of -56)/6. But my book then reduces that to (2 +/- 2 times the sq. root of 14i)/6. But I think in place of the 2 and the sq. root of 14 it could be the sq. root of 7i and the sq. root of four and two, which equals eight. This would then break down to 2 the sq. root of 7i sq. root of 4. But how come this isn't an answer? Why is the book's answer right, and how do you know to choose that one over others? Thanks!!

(2 ± √-56)/6 is right so far

now √-56 = (√-1)(√4)√14) = (2√14)i

so
(2 ± √-56)/6
= (2 ± (2√14)i)/6
= (1 ± √14 i)/3

How come 14 doesn't get reduced to the sq. root of 7i. I would think you'd divide by two on the top and bottom: 6/2=3, 14/2=7).

I don't know that but mine work Is on slope and I don't know it so can you please help :)

1.(1,5)(2,7) 2.(0,1)(3,-8) 3.(2,-3)(4,-2) 4.(2,5)(4,2) 5.(-3,-5)(-1,3) 6.(3,-1)(-6,-4) 7.(4,1)(-4,7) 8.(-1,2)(3,4) 9.(-1,-4)(2,0) 10.(3,-1)(-3,5)

To find the solutions of the quadratic equation 3x^2 - 2x + 5 = 0 using the quadratic formula, you have correctly applied the formula and obtained the expression (2 ± √-56) / 6. However, it seems there is some confusion regarding the simplification of this expression.

Let's break it down step by step:

1. Start with the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -2, and c = 5.

2. Substitute the values into the formula:
x = (2 ± √((-2)^2 - 4 * 3 * 5)) / (2 * 3)
Simplify the discriminant:
x = (2 ± √(4 - 60)) / 6
x = (2 ± √(-56)) / 6

3. At this point, it's important to note that the square root of a negative number results in an imaginary number. To simplify it further, you can rewrite the square root of -56 as the square root of (-1 * 56).

4. The square root of -1 is commonly denoted as "i," which represents the imaginary unit. So, we have:
x = (2 ± √(56 * -1)) / 6
x = (2 ± √(56) * √(-1)) / 6
x = (2 ± √(56) * i) / 6

5. Now, simplify the expression √(56) / 6, which is equivalent to the square root of 14 divided by 3, resulting in:
x = (2 ± (√14) * i) / 6

Therefore, the correct simplified expression for the solutions to the quadratic equation 3x^2 - 2x + 5 = 0 is (2 ± (√14) * i) / 6.

To address your suggestion of using √7i and √(4 * 2), it's worth noting that the imaginary unit "i" cannot be extracted inside the square root. Additionally, the square root of 4 is simply 2, so factoring it out as 2 * √2 would not be accurate in this case.

It's important to follow mathematical conventions and properties when simplifying equations. In this case, the correct simplification of the expression follows the rules for imaginary numbers and the properties of square roots. Your book's answer is accurate because it follows these conventions.