How can I solve a polynomial with a constant term equal to zero?

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To solve the polynomial equation 0 = -x^4 + x^2 + α, where α is a constant, substituting u = x^2 simplifies it to a quadratic equation. This substitution makes it easier to analyze and solve for the roots. Factorization is not effective in this case, but the quadratic form allows for standard solving techniques. This approach is a straightforward method for handling polynomials with a constant term equal to zero. Utilizing substitutions can greatly simplify complex polynomial equations.
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Homework Statement


Hi all.

I have to solve 0=-x^4+x^2+\alpha, where alpha is a constant. I thought of factorizing it, but this won't work.You guys have any tip for solving this?

Thanks in advance.Niles.
 
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If you substitute u=x^2, it turns into a quadratic equation.
 
Ahh, so simple. I hadn't thought of that.

Thanks.
 

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