SOLUTION: Determine the length of the line segment formed by the points of intersection for the system y = 2x^2 − 5x − 6 and y = 3x+ 4. (Leave your answer in simplified radical form)

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Question 1177943: Determine the length of the line segment formed by the points of intersection for the system
y = 2x^2 − 5x − 6 and y = 3x+ 4. (Leave your answer in simplified radical form)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+2x%5E2+-5x+-+6 ...........eq.1
y+=+3x%2B+4........................eq.2
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y+=+2x%5E2+-5x+-+6 ...........eq.1...........substitute y from eq.2
3x%2B+4=+2x%5E2+-5x+-+6
0=+2x%5E2+-5x-3x+-+6-4
2x%5E2+-8x+-+10=0 .......factor
2%28x%5E2+-4x+-+5%29=0 .........factor
2+%28x+-+5%29+%28x+%2B+1%29+=+0
so, solutions are x=5 and x=-1
then
y+=+3%2A5%2B+4=19
y+=+3%2A%28-1%29%2B+4=1+
points of intersection: (5,19) and (-1,1)
the length is equal to distance between (5,19) and (-1,1)
use distance formula
d=sqrt%28%28-1-5%29%5E2%2B%281-19%29%5E2%29
d=sqrt%28%28-6%29%5E2%2B%28-18%29%5E2%29
d=sqrt%28360%29
d=sqrt%2836%2A10%29
d=6sqrt%2810%29=>the length of the line segment formed by the points of intersection for the system