# Algebra II

Explain, without doing any calculations, why there cannot be a Real solution to the equation
p5 + 2x2 + 3px + 7 + 8 = -2:

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1. I suspect typos. The function is littered with junk.

p?
+7+8?

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posted by Steve
2. I will assume p5 is meant to be p^5
and 2x2 is meant to be 2x^2 , then

p^5 + 2x^2 + 3px + 17 = 0
2x^2 + 3px + p^5 + 17 = 0
a quadratic with a = 2 , b = 3p and c = p^5 + 17

for real roots:
9p^2 - 4(2)(p^5 + 17) ≥ 0
9p^2 - 8p^5 - 136 ≥ 0

using Wolfram to solve, I got p < -1.69
http://www.wolframalpha.com/input/?i=9p%5E2+-+8p%5E5+-+136+%3D+0

check your typing, as long as p < -1.69 you will have 2 real solutions each time

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posted by Reiny

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