ParthKohli
What are the roots of \(y = x^2\)?



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goformit100
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dw:1364477055858:dwdw:1364477070806:dw

ParthKohli
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A friend of mine suggests that people don't think that zero is a real solution.

Mertsj
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The roots are the x intercepts. Set y to 0 and you will see that x=0 is a double root which indicates a point of tangency to the x axis at x = 0

Mertsj
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People can think whatever they want. Doesn't make it true.

ParthKohli
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\[x^2 = 0 \implies x = 0\]

goformit100
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You friend is a crazy guy.

ParthKohli
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OK, thank you!

Mertsj
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dw:1364476304306:dw

Mertsj
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yw

ParthKohli
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Thanks, enough to explain.

UnkleRhaukus
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\[y=x^2\]\[x^2y=0\]\[x_{1,2}=\frac{0\pm\sqrt{0^24(1)(y)}}{2(1)}\\=\frac{\pm\sqrt{4y}}{2}\\ =\pm \sqrt y\]

ParthKohli
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Nice solution, but by "roots", I meant zeroes :)

UnkleRhaukus
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\[0=\pm\sqrt0\]

ParthKohli
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Ah, lol!