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mr Goodwill [35]
3 years ago
13

What are the real or imaginary solutions of the polynomial equation x^4-52x^2+576?

Mathematics
2 answers:
klemol [59]3 years ago
5 0
The roots of the polynomial for this case will be x1 = 6, x2 = -6, x3 = 4, x4 = -4.You can solve the polynomial using the resolver after making the variable change u = x ^ 2 so that you have a second degree polynomial. Then return the change to find the missing roots. Attached solution.

jasenka [17]3 years ago
3 0

Answer:

x=-6,-4,4,6.

Step-by-step explanation:

We have been given an equation x^4-52x^2+576=0. We are asked to find the real or imaginary solutions of the given equation.

First of all, we will substitute u=x^2 in our given equation as:

(x^2)^2-52x^2+576=0

(u)^2-52u+576=0    

Now, we  will solve for u as:

u^2-36-16u+576=0

u(u-36)-16(u-36)=0

(u-36)(u-16)=0

u-36=0\text{ (or) }u-16=0

u=36\text{ (or) }u=16  

Now, we will undo substitution as:

x^2=36\text{ (or) }x^2=16

x=\pm\sqrt{36}\text{ (or) }x=\pm\sqrt{16}

x=\pm6\text{ (or) }x=\pm\sqrt4

Therefore, the solutions of our given equation are x=-6,-4,4,6.

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