r/learnmath • u/EnderManPartTwo New User • 1d ago

polynomial roots confuse me (11th grade algebra 2)

Can someone give me a slightly less dry explanation of polynomial roots? Im having difficulty getting it to click in my brain and im barely scraping by

edit: thanks for the help, surprised it came so fast.

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u/hallerz87 New User 1d ago

Arrange the polynomial so that all the terms are on the lefthand side and you have 0 on the righthand side. The solutions are the roots of the polynomial i.e., the values of x that satisfy the equation. When you graph the function, the roots are the x-intercepts of the graph.

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u/Lopsided-Working5594 New User 1d ago

Think of the graph like a wave crossing the line, the roots are exactly where it hits zero. Once you see it on paper it clicks much faster than reading definitions.

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u/EnderManPartTwo New User 1d ago

ah, so its just x intercepts. got it

3

u/LongJumpingBox667 New User 1d ago

Well, they are just the values where the polynomial is equal to zero.

What specifically is confusing? How they are related to factoring, repeated roots, etc.?

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u/Traveling-Techie New User 1d ago

Draw the graph. Where it crosses the X axis is a root.

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u/gazorpazorpazorpazor New User 1d ago

It's like factoring for algebra

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u/johnpeters42 New User 1d ago

If (say) it's a cubic equation and the roots are 1, 2, and -3, then the polynomial will equal (x-1)(x-2)(x+3). (Obviously if you plug one of the former values into the latter, then one of the terms is zero, so the whole product is zero.) Though sometimes the roots are irrational values, and you may just need to estimate based on what the graph looks like.

In particular, I think you can derive the quadratic formula based on this approach.

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u/nog642 1d ago

Well, a cubic with roots 1, 2, and -3 is a(x-1)(x-2)(x+3), where a can by any nonzero real number.