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MArishka [77]
3 years ago
9

What are the solutions of the equation x4 – 5x2 – 36 = 0? use factoring to solve.

Mathematics
2 answers:
algol133 years ago
6 0
X^4 - 5x^2 - 36 = 0
(x^2 - 9)(x^2 + 4) = 0
(x-3)(x+3)(x-2)(x+2) = 0

x = -3, -2, 2, 3
Sergeeva-Olga [200]3 years ago
3 0

Answer:

x = 3, -3, 2i and -2i where i is an imaginary number.

Step-by-step explanation:

We can express the equation x^4-5x^2-36=0 as (x^2)^2-5x^2-36=0, and we can make y = x^2. So, we have the equation y^2-5y-36=0; to find the solutions of this last equation, we should find two numbers such that these numbers sum up to -5 and multiplied result in -36, these numbers are -9 and 4. Therefore y^2-5y-36=0 is equivalent to (y-9)(y+4)=0, but y = x^2, so, (x^2-9)(x^2+4)=0, i.e., (x+3)(x-3)(x^2+4)=0. This last product is equal to zero when x = 3, x = -3 or x^2=-4, x=\pm\sqrt{-4}, i.e., x=\pm2i. Therefore the solutions of the equation x^4-5x^2-36=0 are x = 3, -3, 2i and -2i where i is an imaginary number.

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