# ABC Formula in Cubic Equation

We know that for quadratic equation $$ax^2+bx+c=0$$ , where $$a$$ is a non zero number,

we can use the ABC Formula to determine the value of x.

Here is how we get the value of x.

$$ax^2+bx+c=0$$

$$x^2+\frac{b}{a}x+\frac{c}{a}=0$$

$$x^2+\frac{b}{a}x=-\frac{c}{a}$$

$$x^2+\frac{b}{a}x+(\frac{b}{2a})^2=-\frac{c}{a}+(\frac{b}{2a})^2$$

$$(x+\frac{b}{2a})^2=-\frac{c}{a}+(\frac{b}{2a})^2$$

$$(x+\frac{b}{2a})^2=-\frac{c}{a}+\frac{b^2}{4a^2}$$

$$(x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}$$

$$x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}$$

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Then how about cubic equation $$ax^3+bx^2+cx+d=0$$ ?

Note by Andy Leonardo
2 years, 2 months ago

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- 2 years, 2 months ago

Thankyou Sambhrant , it's really helpful.

- 2 years, 2 months ago