At what points does the line y=3x+2 meet the curve g(x) = 2x^2 -3x-2 ?
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At the point where the line y=3x+2 meets the curve g(x) = 2x^2 -3x-2, the values of x and y are the same.
We equate the two equations:
3x + 2 = 2x^2 - 3x - 2
=> 2x^2 - 6x - 4 = 0
=> x^2 - 3x - 2 = 0
x1 = [-b + sqrt (b^2 - 4ac)]/2a
=> [ 3 + sqrt (9 +8)]/2
=> 3/2 + (sqrt 17) /2
x2 = 3/2 - (sqrt 17) /2
For x = 3/2 + (sqrt 17) /2, y = 13/ 2 + 3*(sqrt 17)/2
For x = 3/2 - (sqrt 17) /2, y = 13/ 2 - (3*sqrt 17)/2
The points of intersection are (3/2 + (sqrt 17)/2 , 13/2 + 3*(sqrt 17)/2) and (3/2 - (sqrt 17)/2, 13/2 - 3*(sqrt 17)/2)
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
We have the line y= 3x+2 and the curve g(x) = 2x^2 -3x-2
We need to find the points of intersection between g(x) and the line y.
Then, we know that the points of intersection must verify the equations of both lines.
==> g(x) = y
==> 2x^2 -3x -2 = 3x+2
Now we will combine all terms on the left side.
==> 2x^2 -6x -4 = 0
We will divide by 2.
==> x^2 -3x -2 = 0
Now we will use the formula.
==> x1= (3+ sqrt(9+8)/ 2= ( 3+ sqrt17)/2==> y1= 3x+2 = (9+3sqrt17)/2 + 2 = (13+3sqrt17)/2
==> x2= (3-sqrt17)/2==> y2= 3x2+2 = (9-3sqrt17)/2 +2 = (13-3sqrt17)/2
Then the points of intersection are:
( (3+sqrt17)/2 , (13+3sqrt17)/2 ) and ( (3-sqrt17)/2 , (13-3sqrt17)/2 )
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