I dont understand.
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4x^4 - 11x^2 - 3
Finding zeros means setting this equal to 0 and solving for x:
4x^4 - 11x^2 - 3 = 0
Let u = x^2:
4u^2 - 11u - 3 = 0
Now, factor as you would any quadratic. Split the b-term:
4u^2 - 12u + u - 3 = 0
(4u^2 - 12u) + (u - 3) = 0
Factor the first term:
4u * (u - 3) + (u - 3) = 0
Re-combine:
(4u + 1) * (u - 3) = 0
So, we have:
4u + 1 = 0 and u - 3 = 0
This means:
4x^2 + 1 = 0 and x^2 - 3 = 0
Solve for x:
4x^2 = -1 and x^2 = 3
x^2 = -1/4 and x^2 = 3
x = i/2 and i/2 and sqrt(3) and -sqrt(3)
Finding zeros means setting this equal to 0 and solving for x:
4x^4 - 11x^2 - 3 = 0
Let u = x^2:
4u^2 - 11u - 3 = 0
Now, factor as you would any quadratic. Split the b-term:
4u^2 - 12u + u - 3 = 0
(4u^2 - 12u) + (u - 3) = 0
Factor the first term:
4u * (u - 3) + (u - 3) = 0
Re-combine:
(4u + 1) * (u - 3) = 0
So, we have:
4u + 1 = 0 and u - 3 = 0
This means:
4x^2 + 1 = 0 and x^2 - 3 = 0
Solve for x:
4x^2 = -1 and x^2 = 3
x^2 = -1/4 and x^2 = 3
x = i/2 and i/2 and sqrt(3) and -sqrt(3)