all odd degree polynomials have at least 1 real root. Explain how we can be sure....
all odd degree polynomials have at least 1 real root. Explain how we can be sure. (the x-intercepts of a polynomial are the same as its real roots. Consider the “end behavior” of odd degree polynomials)
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all odd degree polynomials have at least 1 real root. Explain
how we can be sure....
3. Any polynomial with real coefficients of degree k can be factored com- pletely into first-degree...
3. Any polynomial with real coefficients of degree k can be factored com- pletely into first-degree binomials which may include complex numbers. That is, for any real ao, Q1, ..., āk ao + a1x + a22² + ... + axxk = C(x – 21)(x – z2....(x – zk) for some real C and 21, 22, ... Zk possibly real or complex. Therefore, up to multiplicity, every polynomial of degree k has exactly k-many roots, includ- ing complex roots. Find all...
Using the factorization idea we have been working with, explain carefully how the truth of the...
Using the factorization idea we have been working with, explain carefully how the truth of the statement “Every polynomial of degree at least one has one root can provide a proof for the Fundamental Theorem of Algebra. Consider the complex polynomial p(x) = 2 – 2 in a complex variable 2. You found that there are two real numbers where p'(z) = 322 – 1 is zero. For real inputs these were local extreme values and you can see a...
(1 point) Let P, be the vector space of all polynomials of degree 2 or less,...
(1 point) Let P, be the vector space of all polynomials of degree 2 or less, and let 7 be the subspace spanned by 43x - 32x' +26, 102° - 13x -- 7 and 20.x - 15c" +12 a. The dimension of the subspace His b. Is {43. - 32" +26, 10x - 13.-7,20z - 150 +12) a basis for P2? choose ✓ Be sure you can explain and justify your answer. c. Abasis for the subspace His { }....
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree po...
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree polynomial is irreducible?) 9. 65 points) Find all reducible quartie (le degre ou) polynominls in Talun. (Ht oot s to consider quartic polynomials with no roots. There are not so many of these-look for a pattern that It suffices them -and such a polmomial...
Can someone please help me out State the degree of the following polynomial equation. Find all...
Can someone please help me out
State the degree of the following polynomial equation. Find all of the real and imaginary roots of the equation, stating multiplicity when it is greater than one The degree of the polynomial is Zero is a root of multiplicity is a root of multiplicity 2. Find a polynomial equation with real coefficients that has the given roots -1, 3,-4 The polynomial equation is x3--o Find a polynomial equation with real coefficients that has the...
Help A3: This question illustrates how different bases for spaces of polynomials can help solv- ing...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
At the horizontal intercept x = -3, coming from the (x+3) factor of the polynomial, the...
At the horizontal intercept x = -3, coming from the (x+3) factor of the polynomial, the graph passes directly through the horizontal intercept. The factor (x+3) is linear (has a power of 1), so the behavior near the intercept is like that of a line - it passes directly through the intercept. We call this a single zero, since the zero corresponds to a single factor of the function. At the horizontal intercept x = 2, coming from the (x...
I ALREADY SOLVED THIS! I WANT SOMEONE TO GIVE A DETAILED ANSWERS LIKE VERY DETAILED SOLUTION!...
I ALREADY SOLVED THIS! I WANT SOMEONE TO GIVE A DETAILED
ANSWERS LIKE VERY DETAILED SOLUTION!
ALSO, VERIFY ANSWER WHETHER IT IS RIGHT OR
WRONG!
I ONLY WANT ACCURATE DETAILED CORRECT ANSWER! WRONG AND
SHORT ANSWERS WILL BE DOWNVOTED & REPORTED!
+ 4) Consider the polynomial p(x) = -2x – 5x +x* + 10x + 4x2 – 5x – 3, which can be written in factored form as p(x) = -(2x + 3)(x - 1)(x + 1)2 a. Describe the...
Please MATLAB for all coding with good commenting. (20) Consider the function f(x) = e* -...
Please MATLAB for all coding with good commenting.
(20) Consider the function f(x) = e* - 3x. Using only and exactly the four points on the graph off with x-coordinates -1,0, 1 and 2, use MATLAB's polyfit function to determine a 3' degree polynomial that approximates f on the interval (-1, 2]. Plot the function f(x) and the 360 degree polynomial you have determined on the same set of axes. f must be blue and have a dashed line style,...
10.3 Descartes' Rule of Signs (a) If c. C2, ..., Cm are any m nonzero real...
10.3 Descartes' Rule of Signs (a) If c. C2, ..., Cm are any m nonzero real numbers, and if 2 consecutive terms of this sequence have opposite signs, we say that these 2 terms present a variation of sign. With this concept, we may state Descartes' rule of signs, a proof of which may be found in any textbook on the theory of equations, as follows: Let f(x) = 0 be a polynomial equation with real coefficients and arranged in...
3. Any polynomial with real coefficients of degree k can be factored com- pletely into first-degree binomials which may include complex numbers. That is, for any real ao, Q1, ..., āk ao + a1x + a22² + ... + axxk = C(x – 21)(x – z2....(x – zk) for some real C and 21, 22, ... Zk possibly real or complex. Therefore, up to multiplicity, every polynomial of degree k has exactly k-many roots, includ- ing complex roots. Find all...
Using the factorization idea we have been working with, explain carefully how the truth of the statement “Every polynomial of degree at least one has one root can provide a proof for the Fundamental Theorem of Algebra. Consider the complex polynomial p(x) = 2 – 2 in a complex variable 2. You found that there are two real numbers where p'(z) = 322 – 1 is zero. For real inputs these were local extreme values and you can see a...
(1 point) Let P, be the vector space of all polynomials of degree 2 or less, and let 7 be the subspace spanned by 43x - 32x' +26, 102° - 13x -- 7 and 20.x - 15c" +12 a. The dimension of the subspace His b. Is {43. - 32" +26, 10x - 13.-7,20z - 150 +12) a basis for P2? choose ✓ Be sure you can explain and justify your answer. c. Abasis for the subspace His { }....
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree polynomial is irreducible?) 9. 65 points) Find all reducible quartie (le degre ou) polynominls in Talun. (Ht oot s to consider quartic polynomials with no roots. There are not so many of these-look for a pattern that It suffices them -and such a polmomial...
Can someone please help me out
State the degree of the following polynomial equation. Find all of the real and imaginary roots of the equation, stating multiplicity when it is greater than one The degree of the polynomial is Zero is a root of multiplicity is a root of multiplicity 2. Find a polynomial equation with real coefficients that has the given roots -1, 3,-4 The polynomial equation is x3--o Find a polynomial equation with real coefficients that has the...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
At the horizontal intercept x = -3, coming from the (x+3) factor of the polynomial, the graph passes directly through the horizontal intercept. The factor (x+3) is linear (has a power of 1), so the behavior near the intercept is like that of a line - it passes directly through the intercept. We call this a single zero, since the zero corresponds to a single factor of the function. At the horizontal intercept x = 2, coming from the (x...
I ALREADY SOLVED THIS! I WANT SOMEONE TO GIVE A DETAILED
ANSWERS LIKE VERY DETAILED SOLUTION!
ALSO, VERIFY ANSWER WHETHER IT IS RIGHT OR
WRONG!
I ONLY WANT ACCURATE DETAILED CORRECT ANSWER! WRONG AND
SHORT ANSWERS WILL BE DOWNVOTED & REPORTED!
+ 4) Consider the polynomial p(x) = -2x – 5x +x* + 10x + 4x2 – 5x – 3, which can be written in factored form as p(x) = -(2x + 3)(x - 1)(x + 1)2 a. Describe the...
Please MATLAB for all coding with good commenting.
(20) Consider the function f(x) = e* - 3x. Using only and exactly the four points on the graph off with x-coordinates -1,0, 1 and 2, use MATLAB's polyfit function to determine a 3' degree polynomial that approximates f on the interval (-1, 2]. Plot the function f(x) and the 360 degree polynomial you have determined on the same set of axes. f must be blue and have a dashed line style,...
10.3 Descartes' Rule of Signs (a) If c. C2, ..., Cm are any m nonzero real numbers, and if 2 consecutive terms of this sequence have opposite signs, we say that these 2 terms present a variation of sign. With this concept, we may state Descartes' rule of signs, a proof of which may be found in any textbook on the theory of equations, as follows: Let f(x) = 0 be a polynomial equation with real coefficients and arranged in...
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