SOLUTION: For what values of b will the straight line y=2x+b not intersect the parabola y=x^2+3x-5 ?

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Question 1063607: For what values of b will the straight line y=2x+b not intersect the
parabola y=x^2+3x-5 ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If they did intersect, you would equate the two expressions for y:

x%5E2%2B3x-5=2x%2Bb
x%5E2%2B3x-2x-5-b=0
x%5E2%2Bx-%28b%2B5%29=0

Since you DO NOT want the line and parabola to intersect, then you want this equation to have NO REAL SOLUTIONS, and you must have the discriminant be negative.


1%5E2-4%2A1%2A%28-1%28b%2B5%29%29%3C0

1%2B4%28b%2B5%29%3C0

1%2B4b%2B20%3C0

4b%3C-21

highlight%28b%3C-21%2F4%29---------the requirement so that your given line and parabola do not intersect.