SOLUTION: Find all solutions to x^4 - 7x + 12 =0

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Question 1122436: Find all solutions to x^4 - 7x + 12 =0
Answer by ikleyn(52882) About Me  (Show Source):
You can put this solution on YOUR website!
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graph%28+330%2C+330%2C+-15%2C+15%2C+-5%2C+15%2C%0D%0A++++++++++x%5E4+-+7x+%2B+12%0D%0A%29


Plot y = x%5E4+-+7x+%2B+12



This plot is a  HINT.  It shows you visually that there are no real solutions.


To prove it, use Calculus.


The Calculus will show you, first, that the polynomial has only one min/max point, where the first derivative is zero.


Next, since the polynomial tends to +infinity wnen  x---> infinity  and/or  x ---> -infinity, it becomes clear that the min/max is actually the minimum.


Finally, you can check that the minimum provides a positive value of the polynomial.  //  It is a simple calculation.


Thus you (actually, it was me) proved that the given equation has no real solution.

Solved.