What are the real or imaginary solutions of the polynomials x^4 -­52x^2 + 576 = 0 I don’t think there is a solution, i just want

Question

What are the real or imaginary solutions of the polynomials x^4 -­52x^2 + 576 = 0

I don’t think there is a solution, i just want to know if I’m right before i proceed

0

Answers ( No )

    0
    2021-10-13T23:25:35+00:00

    x^4 -­52x^2 + 576 = 0
    factor: (x
    ²-36)(x²-16)=0
    x²=36 or x²=16
    x=6, -6 or x=4, -4
    all the solutions are real in this case. 

    0
    2021-10-13T23:26:06+00:00

    Answer with explanation:

    The fourth degree Polynomial is:

     \rightarrow x^4-52x^2+576=0\\\\ \text{Splitting the middle term}\\\\\rightarrow x^4-36x^2-16x^2+576=0\\\\\rightarrow x^2*(x^2-36)-16*(x^2-36)=0\\\\\rightarrow (x^2-16)(x^2-36)=0\\\\\rightarrow (x-4)(x+4)(x-6)(x+6)=0\\\\x=4,-4,6,-6

    There are four real Zeroes of the forth degree Polynomial.

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