Hello, I'm studying for the MTEL #47 Practice Test.
I'm having trouble solving problem number 40:
Problem 40: Use the systems of equations to answer the question that follows
y = 2x - 4
y = 2x^2 - 4x - 7
Which of the following expressions represents the x-coordinate of a point in the solution set of the above system of equations.
A. (1+2*sqrt(23)) / 2
B. (2 -sqrt (76)) / 4
C. (3 + (sqrt15)) / 2
The correct answer is in fact C, however, I'm not quite sure how it is obtained.
My strategy was to set the two original equations equal one another like so
2x - 4 = 2x^2 - 4x - 7
Subtract 2x from both sides
-4 = 2x^2 -6x - 7
Add 4 to both sides
0 = 2x^2 - 6x -3
now since A = 2 B = 6 C = -3 I thought you could just plug into the quadratic equation. I also tried to complete the square but that got really messy and I wans't sure how to deal with the square roots.
Any help or guideance with this would be appreciated - I've been struggling to figure it out.
Thanks in advance.
I'm having trouble solving problem number 40:
Problem 40: Use the systems of equations to answer the question that follows
y = 2x - 4
y = 2x^2 - 4x - 7
Which of the following expressions represents the x-coordinate of a point in the solution set of the above system of equations.
A. (1+2*sqrt(23)) / 2
B. (2 -sqrt (76)) / 4
C. (3 + (sqrt15)) / 2
The correct answer is in fact C, however, I'm not quite sure how it is obtained.
My strategy was to set the two original equations equal one another like so
2x - 4 = 2x^2 - 4x - 7
Subtract 2x from both sides
-4 = 2x^2 -6x - 7
Add 4 to both sides
0 = 2x^2 - 6x -3
now since A = 2 B = 6 C = -3 I thought you could just plug into the quadratic equation. I also tried to complete the square but that got really messy and I wans't sure how to deal with the square roots.
Any help or guideance with this would be appreciated - I've been struggling to figure it out.
Thanks in advance.