anonymous
  • anonymous
Quadratic equations: Solve for x: X4 - 5X2 + 4 = 0
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
In quadratic form, the equation would be -5x2 + x4 + 4 = 0
anonymous
  • anonymous
Wouldn´t this equation written in this way x^4-5x^2+4=0
anonymous
  • anonymous
?

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anonymous
  • anonymous
But you would have to have the equation in ax^2 + bx + c form
anonymous
  • anonymous
If this equation has the form above so try to factor out.
anonymous
  • anonymous
-5x2 + x4 + 4 = 0. From here you can use (x^2-4)(x^2-1);
anonymous
  • anonymous
Reminder if ab=0 then a=0 or b=0
anonymous
  • anonymous
X^4-5X^2+4=0 Substitute u=X^2 into the equation. This will make the quadratic formula easy to use. u^2-5u+4=0 u=X^2 Move -4 to the left-hand side of the equation by adding it to both sides. The goal is to have all terms on the left-hand side equal to 0. u^2-5u+4=0 In this problem -1*-4=4 and -1-4=-5, so insert -1 as the right hand term of one factor and -4 as the right-hand term of the other factor. (u-1)(u-4)=0 Set each of the factors of the left-hand side of the equation equal to 0. u-1=0 u-4=0 Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides. u=1 u-4=0 Set each of the factors of the left-hand side of the equation equal to 0. u=1 u-4=0 Since -4 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 4 to both sides. u=1 u=4 The complete solution is the set of the individual solutions. u=1, 4 Substitute the real value of u=X^2 back into the solved equation. X^2=1 X^2=4 Solve the first equation for X. X^2=1 Take the square root of both sides of the equation to eliminate the exponent on the left-hand side. X=+/-sqrt(1) Pull all perfect square roots out from under the radical. In this case, remove the 1 because it is a perfect square. X=+/-1 First, substitute in the + portion of the +/- to find the first solution. X=1 Next, substitute in the - portion of the +/- to find the second solution. X=-1 The complete solution is the result of both the + and - portions of the solution. X=1,-1 Solve the second equation for X. X^2=4 Take the square root of both sides of the equation to eliminate the exponent on the left-hand side. X=+/-sqrt(4) Pull all perfect squXre roots out from under the radical. In this case, remove the 2 because it is a perfect square. X=+/-2 First, substitute in the + portion of the +/- to find the first solution. X=2 Next, substitute in the - portion of the +/- to find the second solution. X=-2 The complete solution is the result of both the + and - portions of the solution. X=2,-2 The solution to X^4-5X^2+4=0 is X=1,-1,2,-2. X=1,-1,2,-2
anonymous
  • anonymous
Two different ways of solving but the same answer.

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