Alberta Free Tutoring And Homework Help For Math 20-2

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The exact solutions to the quadratic equation 0 = 6x2 - 9x - 3 can be written in the form x=p+qr. What is the value of p+q+r?

5 months ago

Answered By Emily D

Some of the info you tried to copy didn't come through so I'm going to take a guess at what the question is. Feel free to ask again if I'm wrong!

0 = 6x2 - 9x - 3

0 = 3*(2x2 - 3x - 1)

This trinomial (2x2 - 3x - 1) cannot be factored further, so we use the quadratic equation.

This gives us the roots

x = 3/4 + sqrt(17/16)

x = 3/4 - sqrt(17/16)


5 months ago

Answered By Emily D

If you don't want to use the quadratic formula, you can complete the square:

2x2 - 3x - 1 = 0 - divide by 2

x- 3x/2 - 1/2 = 0 - add 1/2 to both sides

x2 - 3x/2 = 1/2

divide B (3/2) by two, square it, and add to both sides C = (3/2 * 1/2)2 = 9/16

Note, part of our root is going to be 3/2*1/2 =(3/4)

x2 - 3x/2 + 9/16 = 1/2 + 9/16

 (x - 3/4)2 = 17/16

The square has a positive AND negative root ( sqrt(1) is both +1 and -1)

x - 3/4 = sqrt(17/16)

- (x - 3/4) = sqrt(17/16)

Solving for x, we get

x = 3/4 + sqrt(17/16)

x = 3/4 - sqrt(17/16)


5 months ago

Answered By Emily D

Don't forget to put the two solutions back into your original equation to make sure both = 0!