- #1
logix88
- 12
- 0
I need to get this into (x^2+ x + const) * (x^2+ x + const) format, the answer for this equation is (x^2+x+2)*(x^2+0.0025x+0.005)... I don't know how to get there, NEED HELP EXAM DAY AFTER!
How to factorize x^4 + x^3 + 2.01 x^2 + 0.01 x + 0.01 = 0?
- Thread starter logix88
- Start date
In summary, the conversation is about someone needing help to convert an equation into the format of (x^2+ x + const) * (x^2+ x + const) in order to solve it for an upcoming exam. They are discussing the equation (x^2+x+2)*(x^2+0.0025x+0.005) and how it does not follow the desired format.
- #2
tiny-tim
Science Advisor
Homework Helper
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Hi logix88! 
(try using the X2 tag just above the Reply box)
I don't get it
…
(x2+x+2)*(x2+0.0025x+0.005) quite obviously starts x4 + 1.0025x3 + … , not x4 + x3 + …
(try using the X2 tag just above the Reply box
)logix88 said:
I don't get it
…(x2+x+2)*(x2+0.0025x+0.005) quite obviously starts x4 + 1.0025x3 + … , not x4 + x3 + …
- #3
logix88
- 12
- 0
tiny-tim said:Hi logix88!
(try using the X2 tag just above the Reply box
I don't get it
(x2+x+2)*(x2+0.0025x+0.005) quite obviously starts x4 + 1.0025x3 + … , not x4 + x3 + …
it is correct to 2dp (decimal places)
- #4
ideasrule
Homework Helper
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(x^2+x+2)*(x^2+0.0025x+0.005) is also clearly not in (x^2+ x + const) * (x^2+ x + const) format.
1. How do I factorize x^4 + x^3 + 2.01 x^2 + 0.01 x + 0.01 = 0?
This equation can be factorized by grouping the terms and using the factoring techniques for polynomials. Start by factoring out the greatest common factor, in this case x, to get x(x^3 + x^2 + 2.01x + 0.01) = 0. Then, factor the remaining polynomial using techniques such as grouping, factoring by grouping, or synthetic division.
2. Can this equation be solved using the quadratic formula?
No, the quadratic formula can only be used to solve equations in the form ax^2 + bx + c = 0. This equation has a degree of 4, therefore it cannot be solved using the quadratic formula.
3. Are there any special techniques for factorizing quartic equations?
Yes, there are several techniques specifically for factorizing quartic equations, such as grouping, factoring by grouping, and the AC method. It is important to also look for common factors and use the techniques of factoring by grouping or synthetic division.
4. How many possible solutions does this equation have?
This equation has four possible solutions, since it is a quartic equation. However, not all solutions may be real numbers. Some solutions may be complex numbers.
5. What is the significance of the coefficients 2.01 and 0.01 in this equation?
The coefficients 2.01 and 0.01 are important in determining the factors of this equation. They affect the combinations of factors that can lead to the given equation, and can make the factoring process more complex. It is important to consider all coefficients when factoring a polynomial equation.
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