# Math (Algebra)

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As x ranges over all real values, what is the minimum value of the polynomial x4−14x2+303?

• Math (Algebra) -

If you let u=x^2, you have
u^2 - 14u + 303 = (u-7)^2 + 254

That's just a parabola with vertex at (7,254)

So, the minimum occurs at x=±√7 and is 254.

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