Homework Check?

[ajlm]

Have some homework questions that I'd like to have double checked. I ask only because I don't think I've had enough practice, so I want to make sure I'm right. If I have wrong answers, please just let me know that it is wrong, rather than providing the correct answer.

Thanks!

What are the roots of the equation 2x^2 + 5x -10
x=-5 +/- sqrt (105) / 4

What are the roots of 3x^2-8x-20
x=4/3 +/- sqrt (19) / 3

What are the roots of 3x^2 + 4x + 6
x = -2/3 +/- i sqrt 14 / 3

What are the roots of the equation 2x^2 -8x +16
x=2+/- 2i

What are the roots of 3x^2 + 5x +13
x= -5 +/- i sqrt 131/6

What are the roots of 2x^2 + 4x -18
x=-1 +/- sqrt 10

What are the roots of 2x^2 -15x +30
x=15 +/- i sqrt (15) / 4

What are the roots of 4x^2 - 3x + 9
x=3+/- i sqrt (135) / 8

 

[mmm4444bot]

2x^2 + 5x - 10 = 0

x = -5 +/- sqrt(105)/4 This is correct, but not the way you've typed it.

We need to type grouping symbols, in order to clearly show that both -5 and ±sqrt(105) are divided by 4.

x = [-5 ± sqrt(105)]/4

OR

x = -5/4 ± sqrt(105)/4

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3x^2 - 8x - 20 = 0

x = 4/3 +/- sqrt(19)/3 This is incorrect; try again.

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3x^2 + 4x + 6 = 0

x = -2/3 +/- i sqrt 14 / 3 This is correct, but your typing is sloppy. Is that sqrt(14/3)? No, but that's what it looks like!

x = -2/3 ± i sqrt(14)/3

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?

2x^2 - 8x + 16 = 0

x = 2 +/- 2i This is correct.

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3x^2 + 5x + 13 = 0

x= -5 +/- i sqrt 131/6 This is correct, but not the way you've typed it.

x = [-5 ± i sqrt(131)]/6

OR

x = -5/6 ± i sqrt(131)/6

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2x^2 + 4x - 18 = 0

x = -1 +/- sqrt(10) This is correct.

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2x^2 - 15x + 30 = 0

x=15 +/- i sqrt (15) / 4 This is correct, but not the way you've typed it.

x = [15 ± i sqrt(15)]/4

OR

x = 15/4 ± i sqrt(15)/4

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4x^2 - 3x + 9 = 0

x = 3 +/- i sqrt (135) / 8 Simplify the square root, and type proper grouping symbols.

Overall, I think you're doing just fine.

Also, we can verify solutions ourselves by substituting them into the original equation and checking to see if they lead to a true statement.