Explain, without doing any calculations, why there cannot be a Real solution to the equation
p5 + 2x2 + 3px + 7 + 8 = -2:
I suspect typos. The function is littered with junk.
p?
+7+8?
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
To determine whether there are real solutions to the equation without actually solving it, we need to consider the nature of the equation and its terms. In this case, we have the equation:
p^5 + 2x^2 + 3px + 7 + 8 = -2
To find the real solutions, we typically rearrange the equation to isolate the variable (x), eliminate any constant terms, and use algebraic techniques to solve for x.
However, in this equation, we have an additional variable, p, which introduces further complexity. Since we are given that p is a variable, we cannot easily find a specific value for p without additional information.
Without any specific values or constraints for p, we cannot determine if there are any real solutions to the equation. It is possible that certain values of p may yield real solutions, while others may not.
In summary, without any calculations or additional information about the variable p, we cannot definitively determine whether there are real solutions to the given equation.