Solve the equation x^4 + 4x^2 - 21 = 0 in the complex number system.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The complex roots of the equation x^4 - 4x^2 - 21 = 0 have to be found.

x^4 - 4x^2 - 21 = 0

=> x^4 - 7x^2 + 3x^2 - 21 = 0

=> x^2(x^2 - 7) + 3(x^2 - 7) = 0

=> (x^2 + 3)*(x^2 - 7) = 0

=> x^2 = -3 and x^2 = 7

x^2 = 7 gives real roots.

The complex roots of the equation are `i*sqrt 3` and `-i*sqrt 3`

The complex roots of the equation x^4 - 4x^2 - 21 = 0 are `i*sqrt 3 ` and `-i*sqrt 3`

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