How to find the solution of cubic equation?
Answers
Answer:
Method One of Three:
Solving Cubic Equations without a Constant
1
Check whether your cubic contains a constant (a d value). Cubic equations take the form ax^{3}+bx^{2}+cx+d=0. However, the only essential requirement is x^{3}, which means the other elements need not be present to have a cubic equation.[1]If your equation does contain a constant (a d value), you'll need to use another solving method.If a=0, you do not have a cubic equation.[2]
2
Factor an x out of the equation. Since your equation doesn't have a constant, every term in the equation has an x variable in it. This means that one x can be factored out of the equation to simplify it. Do this and re-write your equation in the form x(ax^{2}+bx+c).[3]For example, let's say that your starting cubic equation is 3x^{3}-2x^{2}+14x=0Factoring a single x out of this equation, you get x(3x^{2}-2x+14)=0
3
Factor the resulting quadratic equation, if possible. In many cases, you will be able to factor the quadratic equation (ax^{2}+bx+c) that results when you factor the x out. For example, if you are given x^{3}+5x^{2}-14x=0, then you can do the following:[4]Factor out the x: x(x^{2}+5x-14)=0Factor the quadratic in parentheses: x(x+7)(x-2)=0Set each of these factors equal to0. Your solutions are x=0,x=-7,x=2.
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