Find the range of values of x for which the equation in
y, 2x^2 − 3xy + y^2 − 5x + 11 =0
will have real roots. Find also for what values of y the equation in x will have real roots.

Question

Find the range of values of x for which the equation in 
y,  2x^2 − 3xy + y^2 − 5x + 11 =0 
will have real roots. Find also for what values of y the equation in x will have real roots.

anonymous · Answer

Complete the square?  Or quadratic equation!

aonz · Answer

complete the square is better i think

anonymous · Answer

So if you let $x$ be the variable then $\color{red}a, \color{blue}b, \text{ and } \color{green} c$ are:$$
\color{red} {2}x^2 + \color{blue}{ (-3y-5)}x +\color{green}{ y^2+11 }
$$

aonz · Answer

ooh? hmm i think i can solve this now. Gimme a min

aonz · Answer

i got discriminant to equal to y^2 + 30y - 63

anonymous · Answer

Is that what you got for $b^2 - 4ac$?

aonz · Answer

now i have $$y = -15 \pm 12\sqrt{2}$$

anonymous · Answer

For real roots we want $b^2-4ac \geq 0$

aonz · Answer

yea

anonymous · Answer

Well, you want to know when the equation of $y$ is above $0$.

anonymous · Answer

Roots will only help you know when it changes from positive to negative.

aonz · Answer

ok i got both my y things. How do we find the x ones?

anonymous · Answer

Okay so for what values of $y$ does $x$ have real roots?

aonz · Answer

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