Question
$$-\frac{3}{50}x^6+\frac{68}{25}x^5-\frac{191}{4}x^4+\frac{2696}{7}x^3-\frac{2877}{2}x^2+2453x+15164 = 1000000$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -\frac{3}{50}x^6+\frac{68}{25}x^5-\frac{191}{4}x^4+\frac{2696}{7}x^3-\frac{2877}{2}x^2+2453x+15164 &= 1000000&& \text{multiply ALL terms by } \color{blue}{ 700 }. \\[1 em]-700 \cdot \frac{3}{50}x^6+700\frac{68}{25}x^5-700\frac{191}{4}x^4+700\frac{2696}{7}x^3-700\frac{2877}{2}x^2+700\cdot2453x+700\cdot15164 &= 700\cdot1000000&& \text{cancel out the denominators} \\[1 em]-42x^6+1904x^5-33425x^4+269600x^3-1006950x^2+1717100x+10614800 &= 700000000&& \text{move all terms to the left hand side } \\[1 em]-42x^6+1904x^5-33425x^4+269600x^3-1006950x^2+1717100x+10614800-700000000 &= 0&& \text{simplify left side} \\[1 em]-42x^6+1904x^5-33425x^4+269600x^3-1006950x^2+1717100x-689385200 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver