Solving A Nice Polynomial Equation

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PLAYLISTS 🎵 :

[mbmillermo]

This is what I did: x²-x+¼ + y² = (x-½)² + y² = 0. And you're done because that's the equation for a circle with a center at (½, 0) having a radius of zero.

[ianfowler]

When you transpose all the terms to the Left Side, you already have a perfect square.
(x - 1/2)^2 + y^2 = 0. See Mike below.

When a quadratic in this form (circle) has only a 1 point solution, we call this a "degenerate" circle.This "degenerate" classification can also apply to an ellipse and a hyperbola whereas a degenerate parabola is a straight line.

[ngdluu]

we also know that (x+a)^2+(y+b)^2=R^2 is the formula of a circle. So this equation is a a circle with R=0 so it shows us a point in the coordinate plane

[apocwiar]

The Plane touching The Paraboloid at one specific point. Nice

[alextang]

We can think that this is a line intercept a circle. This thought is more interesting than using a algebra to solve it! 😊😊😊😊😊😊

[scottleung]

Cool - I used the second method, except that I didn't get rid of the fraction. I was actually able to work with the 1/4 quite easily.

[burgazadaeczanesi]

İt is equation of a circle whose radius is zero (x-1/2)^2+y^2=0 and center is x=1/2 and y=0

[FrancisZerbib]

As always thank you for the great video. As opposed to Desmos, GeoGebra shows the correct result

[srividhyamoorthy]

Why is it that it seems hard but really really easy its just the correct set of ideas that have to be put together in order to solve it

[mega_mango]

x = 1/2 + k
1/4 + k² + k + y² = k + 1/2 - 1/4 = k + 1/4 (//-(k + 1/4))
k² + y² = 0.
k² = -y²
k = ±iy
x = 1/2 ± yi
If we talk about real solution it's x = 1/2, y = 0

[BlaqRaq]

I’m still confused!!
How do you know which is the first method??
😂😂😂😂

[loganpankonin]

You could written this in the standard form of a circle and has a radius of 0