How to Solve a Quartic Equation by Hand

  • Thread starter phillyolly
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In summary, the general approach to solving a quadratic equation is to rearrange the terms and use the quadratic formula or factoring. The discriminant can be used to determine the number of real solutions for x. Mental math is not sufficient for solving this equation, but a graphing calculator can be used. To check the validity of a solution, it can be plugged back into the original equation.
  • #1
phillyolly
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Hi!

I have been solving a problem and got an equation:
15x^4-30x^2+1=0

Do you know how to solve such equation for x by hand without using sophisticated math tools?
 
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  • #2
you can assume x^2 = t
so you get a quadratic in t... which i assume you can easily:wink: solve and get two values of t.
using these you will then get 4 values in x(some of which may be rejected according to the problem)
 
  • #3
This is a great idea! Thank you! ;-)
 

FAQ: How to Solve a Quartic Equation by Hand

1. What is the general approach to solving this equation?

The general approach to solving this equation is to first rearrange the terms so that the equation is in the form of a quadratic equation, with the highest degree term on the left side and a constant term on the right side. Then, you can use the quadratic formula or factoring to solve for the values of x.

2. How do I know if there are any real solutions for x?

To determine if there are any real solutions for x, you can use the discriminant, which is the value under the square root in the quadratic formula. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. And if it is negative, there are no real solutions.

3. Can this equation be solved using only mental math?

No, it is not possible to solve this equation using only mental math. The equation requires the use of algebraic techniques such as factoring or the quadratic formula, which cannot be done mentally.

4. Can I use a graphing calculator to solve this equation?

Yes, a graphing calculator can be used to solve this equation. You can enter the equation into the calculator and use the intersect function to find the x-intercepts, which are the solutions to the equation.

5. Is there a way to check if my solution for x is correct?

Yes, you can check your solution by plugging it back into the original equation. If it satisfies the equation and gives a true statement, then it is a valid solution. If it does not satisfy the equation, then it is not a valid solution.

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