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 $ax^3+bx^2+cx+d=0$ ?

#Algebra

Easy Math Editor

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Comments

You will get your answers here

Sabhrant Sachan - 4 years, 12 months ago

Thankyou Sambhrant , it's really helpful.

Andy Leonardo - 4 years, 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$