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 $(-5-sqrt17,2) and (-5+sqrt17,2)$ .

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