5. (114, Exercise 12) Let f(2) € R[2] (a) If deg((f(t)) = 2, how many real...

Question

Question

5. (114, Exercise 12) Let f(2) € R[2] (a) If deg((f(t)) = 2, how many real roots can f(2) have? (b) If deg(f(2)) = 3, how man

math Advanced-Math

Answer 1

Answer #1

5. flv) E R [2] . then f.(a) has (a) since dag (f(x)) f(n)) = 2 real either roots two or real be roots no (6) then f(x) has e

Answer 2

Answer #2

We know that f(x) is contained in R(x).

a.

If f(x) has degree of two then, it will have two real roots or two complex roots.

b.

If f(x) has degree of three then, it will have three real roots or one real root along with two complex roots.

answered by: Tulsiram Garg

Answer 3

Similar Homework Help Questions

Let F = R. Let f = t3 – ajta – azt Az E R[t]. Show:...

Let F = R. Let f = t3 – ajta – azt Az E R[t]. Show: (a) The discriminant A = -4aſaz + a až – 18a1a2a3 + 4a3 – 27az. (b) f has multiple roots if and only if A = 0. (c) f has three distinct real roots if and only if A >0. (d) f has one real root and two non-real roots if and only if A < 0.
Theorem 14.7. If f(x) € R[x] is an irreducible polynomial, then deg(f(x)) is either 1 or...

Theorem 14.7. If f(x) € R[x] is an irreducible polynomial, then deg(f(x)) is either 1 or 2. We can determine which quadratic polynomials in R[x] are irreducible by using the quadratic formula and checking for real roots. Activity 14.8. Factor f(x) = 2 – 4.x in R[2] into a product of irreducible polynomials in R[2].
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei,...

Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei, and consider the autonomous differential equation y(t) = f(y(t)). fly) у FIGURE 1. The function f(y) for Problem 4. (a) How many constant solutions does the above differential equation have ? (b) Study whether the behaviour of each of the constant solutions of the differential equation y(t) = f(y(t)) is stable, unstable or semistable. (c) Discuss the long-term behaviour of all solutions y(t) to...

Exercise 5. Let f(t) denote the 2-periodic function f(t) = 1+2 - <t< . a) Make...

Exercise 5. Let f(t) denote the 2-periodic function f(t) = 1+2 - <t< . a) Make a representative plot of f(t) showing at least 3 periods. b) Using the numerical integration routine you wrote in your Home work 1 (Exercise 3) compute approx- imately the values of the Fourier series coefficients all of f() for k in the range -20 to 20. c) Make a plot of laul
Please answer with this varied parameter --> (now let T=900 deg F, R=95%) Consider a 3.5-in.-diameter...

Please answer with this varied parameter --> (now let T=900 deg F, R=95%) Consider a 3.5-in.-diameter steel bar having Su=97 ksi and Sy=68 ksi and machined surfaces. Estimate the fatigue strength for (1) 10^6or more cycles and(2) 5*10^4cycles for (a) bending, (b) axial, and (c) torsional loading.
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and...

Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and Ui = {p(z) : p(z) a? + bz5, for abe R}, find a subspace U2 such that R deg< 5 = Ui φ Ủy Is this U2 unique? (g) If V be a finite dimensional vector space, dim V = n and B = 〈ui,u2, . . . , un) is a basis of V, then show that:

Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) ...

Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function? Prob 4. Let V be a finite-dimensional real vector space and let T є C(V). Define f : R R by f(A) :- dim range (T-λΓ Which condition on T is equivalent to f being a continuous function?
5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How...

5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How many zeros (real and complex, possibly with repetition) does f(x) have? What theorem did you use to get this answer? (b) (3 points) Determine all possible rational roots of p(x). (c) (2 points) What values from part (b) are actually roots of p(x)? You do not need to justify your answer. (d) (6 points) Find all other real and complex roots of p(x). Show...
Definition A: Let R be ring and r e R. Then r is called a zero-divisor...

Definition A: Let R be ring and r e R. Then r is called a zero-divisor in Rifr+0r and there exists SER with s # OR and rs = OR. Exercise 1. Let R be a ring with identity and f € R[2]. Prove or give a counter example: (a) If f is a zero-divisor in R[x], then lead(f) is a zero-divisor in R. (b) If lead(f) is a zero- divisor in R[x], then f is a zero-divisor in R[2]....

be a coordinate function for 1.) (Coordinate functions) Let f: R a (a) (Exercise 3A) Prove...

be a coordinate function for 1.) (Coordinate functions) Let f: R a (a) (Exercise 3A) Prove that -f is a coordinate function as well. (5 (b) For which real numbers a, b e R is a f+b a coordinate function? (c) Let g:E → R be a coordinate function. Prove that there exists a line ( points) Justify your answer with a proof. (10 points) real number b E R, such that g-f+b or gf+b. (10 points)