Question

How many solutions does this equation have? –4 u = 13u⁹ − 12u

Answer 1

The equation -4u = 13u⁹ - 12u can be rearranged to form a polynomial equation, which upon factoring out shows one solution, u=0. The remaining factor is an eighth degree polynomial, which can have up to 8 real solutions, for a potential total of 9 solutions.

Step-by-step explanation:

The equation presented is a polynomial equation of the form –4u = 13u9 – 12u. To find out how many solutions this equation has, we need to rearrange it into a standard form and then use the Fundamental Theorem of Algebra. Let's move all terms to one side:

0 = 13u9 – 12u + 4u

0 = 13u9 – 8u

Now, by factoring out u, we have:

0 = u(13u8 – 8)

This shows that u=0 is one solution. Now, we need to consider the equation 13u8 – 8 = 0 to find the remaining solutions. Without specifying the exact solutions, we can say that this eighth degree polynomial equation can have up to 8 real solutions. Therefore, the total number of solutions can be up to 9 including the solution where u=0, but without further information or numerical methods, we cannot specify the exact number of real solutions.