Inequality question?

[momoko]

Given that the line y = 2x + c does not intersect the curve 2xy + 6 = 0, find the range of values of c.

So does this mean 2xy + 6 = 0 has no real roots? But how do I go about solving this question?
Sorry if it's a silly to ask but I don't know what I am supposed to do.

Thank you in advance!

 

[Deleted member 4993]

Given that the line y = 2x + c does not intersect the curve 2xy + 6 = 0, find the range of values of c.

So does this mean 2xy + 6 = 0 has no real roots? But how do I go about solving this question?
Sorry if it's a silly to ask but I don't know what I am supposed to do.

Thank you in advance!

2xy + 6 = 0 has no real roots - true statement but does not help you solve the problem.

To get a direction - plot y = -3/x.

Now visualize which intercepts (c) will make it possible for the line to intersect the curve.

To do it algebraically, equate those to "y s" and find th condition for intersection.

From that find the condition for non-intersection.

 

[garf]

to replace one of the equations, in the other, and to see that values can take c so that it is truth the equation
y=2x+c
2xy=6
2x(2x+c)=6
4x[sup:te67nu5f]2[/sup:te67nu5f]+2cx-6=0
a=4
b=2c
c=-6