Write True If The Statement Is True. Otherwise, Modify The Underlined Word(S) To Make It True. 2. Every Polynomial Equation Of Degree N Has N 2013 1 R
Write TRUE if the statement is true. Otherwise, modify the underlined word(s) to make it true. 2. Every polynomial equation of degree n has n – 1 real roots.
Polynomial Equation:
"Every polynomial equation of degree n has n - 1 real roots." This statement is false and in order to make it a true statement it should be... "every polynomial equation of degree n has at most n real roots" which is a consequence of the Fundamental Theorem of Algebra.
Definition:
A polynomial equation is any polynomial equated to zero.
Examples:
- x - 2 = 0
- x² + 2x + 5 = 0
- 5x + 1 = 0
- x³ - 2x² - 4x + 8 = 0
- x(x - 4) = 0
Explanation:
x - 2 = 0 the number of root(s) is just 1 since it is a polynomial of the first degree.
x² + 2x + 5 = 0 the number of root(s) is 2 since it is a polynomial of the second degree.
5x + 1 = 0, there is only 1 root because it is a polynomial equation of the first degree.
x³ - 2x² - 4x + 8 = 0 have 3 roots since its highest degree is 3.
x(x - 4) = 0 have 2 roots because it is a polynomial equation of the second degree.
Code: 10.3.1.2.3
For more information regarding polynomial equations, go to the following links:
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