Question
x^4 + 6x^2 = -8 Solve the equation.
Answers
Ms. Sue
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Jai
Place all terms to left side of equation:
x^4 + 6x^2 = -8
x^4 + 6x^2 + 8 = 0
This is factorable. But how do you factor this?
What we'll do is list all the factor pairs of 8 and from these, we choose the pair which has a sum of 6.
1 x 8 | 2 x 4 | -1 x -8 | -2 x -4
Here, we can see that the pair with sum of 6 is 2 x 4.
We rewrite the quadratic equation as such:
(x^2 + 2)(x^2 + 4) = 0
We can equate each factor to zero:
(x^2 + 2) = 0
x^2 = -2
x = sqrt(-2)
(x^2 + 4) = 0
x^2 = -4
x = 2*sqrt(-1)
x^4 + 6x^2 = -8
x^4 + 6x^2 + 8 = 0
This is factorable. But how do you factor this?
What we'll do is list all the factor pairs of 8 and from these, we choose the pair which has a sum of 6.
1 x 8 | 2 x 4 | -1 x -8 | -2 x -4
Here, we can see that the pair with sum of 6 is 2 x 4.
We rewrite the quadratic equation as such:
(x^2 + 2)(x^2 + 4) = 0
We can equate each factor to zero:
(x^2 + 2) = 0
x^2 = -2
x = sqrt(-2)
(x^2 + 4) = 0
x^2 = -4
x = 2*sqrt(-1)