What is the verbal expression for this problem?
2 answers:
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Definition
Functions have zeros or x-values that generate function values equal to zero.
Equations have roots or solutions that can be substituted into the polynomial in order to generate a value equal to zero.
Given:
To convert this to an equation, we set f(x) equal to zero i.e
The resulting equation is:
Answer:
The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i
Step-by-step explanation:
1) This claim is mistaken.
2) The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i with real coefficients.
For example:
3) Every time a polynomial equation, like a quadratic equation which is an univariate polynomial one, has its discriminant following this rule:
We'll have <em>n </em>different complex roots, not necessarily 2i.
For example:
Taking 3 polynomial equations with real coefficients, with
2.2) For other Polynomial equations with real coefficients we can see other complex roots ≠ 2i. In this one we have also -2i
Answer:
Take as the projection of u onto v and
as the vector such that b+w =u
Step-by-step explanation:
The formula of projection of a vector u onto a vector v is given by
, where
is the dot product between vectors.
First, let b ve the projection of u onto v. Then
We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]
By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.
We have that . Then this vectors are orthogonal, and thus, w and b are orthogonal.