The 4th Degree Polynomial equation computes a fourth degree polynomial where a, b, c, d, and e are each multiplicative constants and x is the independent variable.
`y = ax^4 + bx^3 +cx^2 + dx + e`
INSTRUCTIONS: Enter the following:
4th Degree Polynomial Value (y): The calculator returns the associated value for x in the polynomial
The equation of a fourth degree polynomial is:
`y = ax^4 + bx^3 +cx^2 + dx + e` (showing the multiplications explicitly: `y = a*x^4 + b*x^3 + c*x^2 + d*x + e`)
The equation is called "fourth degree" because it has an `x^4` term. If it also had an `x^5` term in it, it would be called a fifth degree polynomial.
Note that the five terms could be thought of as each term having a multiplying constant: a, b, c, d, and e
So, the form of the fourth degree polynomial could be re-written more explicitly to be:
`y = a*x^4 + b*x^3 + c*x^2 + d*x^1 + e*x^0`
We can make up examples values of a, b, c, d, and e to form an infinite number of variations on a fourth degree polynomial. The multiplicative constants, a, b, c, d, and e, can have integer or decimal values:
ex. `y = 5x^4 + 3x^3 + 6x^2 + 7x + 23` ; if `x = 5`, this evaluates to `y = 3708`
ex. `y = 1.1x^4 + 3.7x^3 + 2.1x^2 + 0.4x + 22.2` ; if `x = 4.5`, this evaluates to `y = 854.75625`
The multiplicative constants for b, c, d and e can also be zero. Technically, the a constant can't be zero if the equation is to be called a "fourth degree polynomial" but this brings up an interesting point: a lower degree polynomial is only a higher degree polynomial with all the higher order terms having multiplicative constants equal to zero. `a*x^4 + b*x^3 + c*x^2 + d*x + e = 0*x^6 + 0*x^5 + a*x^4 + b*x^3 + c*x^2 + d*x + e`
Here are two examples of the b, c, d, or e constants being zero.
Here is an example of one of the constants, the c constant, being a negative multiplier:
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