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Mr Davis 97
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I have the equation ##2t^{6} + 13t^{4} - 36 = 0##. How can I solve this for the real roots without using a CAS? That is, by hand?
A 6th degree equation is a polynomial equation that contains a variable raised to the 6th power. It can be written in the form ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g = 0, where a, b, c, d, e, f, and g are constants and x is the variable.
Unlike quadratic, cubic, and quartic equations, there is no general formula to solve 6th degree equations. Therefore, it requires a combination of algebraic techniques, such as factoring, the rational root theorem, and the method of undetermined coefficients. It may also involve the use of advanced mathematical concepts, such as complex numbers.
Yes, all 6th degree equations have at least one real or complex solution. However, some equations may have multiple solutions or no real solutions depending on the values of the coefficients.
Yes, 6th degree equations are commonly used in physics, engineering, and other sciences to model various phenomena and relationships. They can also be used in finance and economics to calculate interest rates, growth rates, and other financial variables.
No, there is no single method that can be used to solve all 6th degree equations. The approach to solving each equation may vary depending on its specific form and the techniques that are most suitable for it.