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Snezhnost [94]
3 years ago
9

What are the roots of the polynomial equation 3x^4+12x^2=6x^3

Mathematics
1 answer:
Dominik [7]3 years ago
7 0
Factor the equation to give
3x^4+12x^2=6x^3
3x^4+12x^2-6x^3=0
x^2(3x^2+12-6x)=0
By the zero product property, either x^2=0 or (3x^2+12-6x)=0 or both.
If x^2=0, then x=0
if (3x^2+12-6x)=0, we use the quadratic formula to solve for x
where x=1 ± √ (3) i

Answer: the roots of <span>3x^4+12x^2=6x^3 are {0 (multiplicity 2), 1+&radic;3 i, 1-&radic;3 i}</span>
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