i am doing some exam prep for my functions class but i can't seem to remember how to solve equations with a degree of 4 or higher. Here is the example i am working on. Thank in advanced.
2x^4 + 11x^3 + 9x^2 – 14x – 8 = 0
i am doing some exam prep for my functions class but i can't seem to remember how to solve equations with a degree of 4 or higher. Here is the example i am working on. Thank in advanced.
2x^4 + 11x^3 + 9x^2 – 14x – 8 = 0
Use synthetic division on suspected roots to confirm they are roots and reduce the power of the polynomial remainder.
For this particular problem, a trick:
When all of the coefficients of a polynomial sum to 0, then 1 is one of the roots. Confirm with division and then work on the third degree polynomial that remains.
If you want to solve the long way, use this calculator here that shows the 4 real roots and how to get there:
Solving Quartic Equations
This shows how to break the quartic into a cubic and go from there if you decide not to take the synthetic division route.