Does the parabola #y= -1/2x^2 - 5x - 10# ever intersect the line #y= 2#?

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Answer 1 · 2018-04-14T07:22:06

#" Yes, at the points "(-5-sqrt17,2) and (-5+sqrt17,2)#.

If it does, then the #x"-co-ordinates"# of their points of

intersection (if any) must satisfy the following eqn. :

#2=-1/2x^2-5x-2#.

To get rid of fractions, multiplying by #2#, we have,

#4=-x^2-10x-4, or, x^2+10x+8=0#.

#:. x^2+2*x*5+5^2-25+8=0, i.e., #.

# (x+5)^2=25-8=17#.

#:. x+5=+-sqrt17#.

#:. x=-5+-sqrt17#.

The corresponding #y"-co-ordinate"# is already known to be #2#.

Accordingly, the given curves do intersect each other at the

points #(-5-sqrt17,2) and (-5+sqrt17,2)#.