Possible values of x²

Biquadratic equations are in a sense, quadratic equations of x². Therefore, there should be one or two possible value of x² in a biquadratic equation. Just like when we have to look for the value of x in a quadratic equation, we can look for the value of x² in a biquadratic equation using quadratic formula, factorization and completing the square.

All you have to do is to check any check boxes related to looking for possible value of x² in a biquadratic equation ( see the picture above ). Then click as HTML to tell Orimath Biquadratic Solver to solve the problem for you and tell you the steps required to get the answer.

Purchase BiQuadratic Solver for $8.00

Answer by Orimath Quadratic Solver :

Question Number 2 :
For this equation ( x² + 3 ) ( x² - 2 ) = x² - 2 , answer the following questions :

	A.	Find two possible value of x² using Quadratic Formula !
	B.	Find two possible value of x² using Factorization !

Answer Number 2 :

First, we must turn this equation ( x² + 3 ) ( x² - 2 ) = x^2 - 2 into ax²+bx+c=0 form.
	( x² + 3 ) ( x² - 2 ) = x² - 2 , expand the left hand side.
	<=> x² ( x² - 2 ) + 3 ( x² - 2 ) = x² - 2
	<=> ( x⁴ - 2x² ) + ( 3x² - 6 ) = x² - 2
	<=> x⁴ + x² - 6 = x² - 2 , move everything in the right hand side to the left hand side.
	<=> x⁴ + x² - 6 - ( x² - 2 ) = 0
	<=> x⁴ + x² - 6 + ( - x² + 2 ) = 0
	<=> x⁴ - 4 = 0

The equation x⁴ - 4 = 0 is already in ax⁴+bx²+c=0 form.
By matching the constant position, we can derive that the value of a = 1, b = 0, c = -4.

1A . Find two possible value of x² using Quadratic Formula ! Back To Question

Use the formula,

x²_[1,2] =

-b		(b²-4ac)

2a

We had know that a = 1, b = 0 and c = -4,

we just need to subtitute the value of a,b and c in the abc formula.

Which produce x²_[1,2] =	- (0)	(0)² - 4 (1) (-4) )

	2 (1)

So x²_[1,2] =	0	(0 + 16)

	2

So we get x²_[1,2] =	0	16

	2

So we get x₁² = ( 4 )/(2) and x₂² = ( - 4 )/(2)

So we got the answers as x₁² = 2 and x₂² = -2

2B . Find two possible value of x² using Factorization ! Back To Question

x⁴ - 4 = 0 , factorize the left hand side.

( x² - 2 ) ( x² + 2 ) = 0

So we got the answers as x₁² = 2 and x₂² = -2

Purchase BiQuadratic Solver for $8.00

Design and Concept By CreArtSolution

Possible values of x2

Possible values of x²