What does it mean when it says Roots (order) for a function eg. -x^3-2x^2+15x+36
What i mean is how do you the answer.
the highest exponent is the order...and the number of roots
a root is a value that makes the function equal to zero
you can test values for roots
... 4 works here
divide the function by (x - 4) to factor out the known root
... this leaves a quadratic
... use the quadratic formula for the last two roots
so if i found that the roots are -3 and 4 how would i write that?
-3(order 2), 4
because at -3 the function acts like a quadratic but at 4 it acts linear.
-3 is not a root
the roots are ... -3±i
4, -3+i, -3-i
the highest exponent is the degree
the order of a root is the number of times it appears.
So, you have three roots of degree 1.
Any polynomial of degree n has exactly n roots, though all may not be unique (order 1).
When the term "Roots (order)" is mentioned for a function, it refers to the solutions or values of the variables that make the function equal to zero. In other words, the roots of a function are the values of the variable that satisfy the equation of the function.
To find the roots of the function -x^3 - 2x^2 + 15x + 36, you can follow these steps:
1. Set the function equal to zero:
-x^3 - 2x^2 + 15x + 36 = 0
2. Rearrange the equation to bring all the terms to one side to obtain a polynomial in standard form:
-x^3 - 2x^2 + 15x + 36 = 0
This step is already done in the given equation.
3. Factorize the polynomial:
Factorizing the polynomial might help in identifying the roots. However, in this case, factoring the polynomial is a bit challenging, as it does not have any evident common factors.
4. Apply different root-finding methods:
There are multiple methods for finding the roots of a function, such as the rational root theorem, synthetic division, or numerical methods like Newton's method or Bisection method.
In this case, applying numerical methods might be more efficient. You can use software like graphing calculators or equation solvers, or programming languages with built-in functions to find the roots numerically.
Keep in mind that the number of roots depends on the degree of the polynomial. For a polynomial of degree n, there can be up to n roots.
By following these steps or using numerical methods, you can determine the roots of the given function and find the values of the variable that make the function equal to zero.