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Solve 2x^4 + 16x² + 24 = 0?
Solve 2x^4 + 16x² + 24 = 0. Find all complex zeros and show your work
4 Answers
- NiallLv 76 years ago
Divide through by 2:
x^4 + 8x^2 + 12 = 0
Let x^2 = y:
y^2 + 8y + 12 = 0
Factor it out:
(y + 6)(y + 2) = 0
Substitute x^2 back for y:
(x^2 + 6)(x^2 + 2) = 0
Set each piece to equal zero and solve:
x^2 + 6 = 0
x^2 = -6
x = isqrt(6), -isqrt(6)
x^2 + 2 = 0
x^2 = -2
x = isqrt(2), -isqrt(2)
---------
Overall:
x = isqrt(2), -isqrt(2), isqrt(6), -isqrt(6)
- ranjankarLv 76 years ago
2 ( x^4 + 8x^2 + 12) = 0
2 ( x^4 + 2x^2 + 6x^2 +12) = 0
2 ( x^2 ( x^2 + 2) +6 ( x^2 +2) ) = 0
2 ( x^2+6) ( x^2 +2) = 0
x = i \/6 OR - i \/6 OR i \/2 OR - i \/2 ANSWER
