What is depressed equation in math?
What is depressed equation in math?
[di′prest i′kwā·zhən] (mathematics) An equation that results from reducing the number of roots in a given equation with one unknown by dividing the original equation by the difference of the unknown and a root.
What is a depressed equation in synthetic division?
Depressed equation. The equation resulting from reducing the number of roots in an equation. For example, one root of G(x) = x3 – 3×2 + 4x – 2 = 0 is 1. Thus x – 1 is a factor of G(x).
What is a depressed cubic?
Depressed cubic gives a cubic (in t) that has no term in t2. After dividing by a one gets the depressed cubic equation. with. The roots of the original equation are related to the roots of the depressed equation by the relations. for .
Is a factor of the polynomial function?
A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x2 – 4. The factorization of a polynomial is its representation as a product its factors. For example, the factorization of x2 – 4 is (x – 2)(x + 2).
What does remainder theorem state?
The Remainder Theorem Definition states that when a polynomial is p ( a ) is divided by another binomial ( a – x ), then the remainder of the end result that is obtained is p ( x ).
What is a ninth degree polynomial called?
For higher degrees, names have sometimes been proposed, but they are rarely used: Degree 8 – octic. Degree 9 – nonic. Degree 10 – decic.
How to find a depressed polynomial in MATLAB?
The Matlab function depressedcubic.m transform it into the “depressed” cubic form p2 (x) This function checks if the input is a valid cubic polynomial (expressed as a 4-vector as in Matlab format) with the coefficient of the cubic term non zero.
Is there a function to obtain the depressed cubic polynomial?
Function to obtain the “depressed” cubic polynomial, from the general cubic form. Originally intended to process monic cubic forms, this new version can process a general cubic form. Checked for sign issues, and corrected the expression for “k2” (description above).
What happens when you divide a polynomial by a factor?
When you divide a polynomial by one of its binomial factors, the quotient is called a depressed polynomial. Above, we’re dividing a polynomial by one of its factors (x – 4). Because we’re dividing by a factor, we end up with a remainder of 0.