Algebra

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Let r be a root of x^3 - 2x + 5 = x^3 - x^2 + 9. Show that none of r, r^2, or r^3 is irrational.

Guest Apr 14, 2023

gb1falcon · Answer 1 · 2023-05-04T06:57:03

Simplify the expression: $x^2-2x-4=0$ . Use the quadratic formula to get

$\frac{2 \pm \sqrt{(-2)^2-4\cdot1\cdot(-4)}}{2}$

$\frac{2 \pm \sqrt{4-(-16)}}{2}$

$\frac{2 \pm \sqrt{20}}{2}$

$1 \pm \sqrt{5} = r$

So r is irrational, so this cannot be done.