Let $f(x)= x^3+3x^2+6x+2009$ and $$g(x)=\dfrac{1}{x-f(1)}+\dfrac{2}{x-f(2)}+\dfrac{3}{(x-f(3)}.$$ The number of real solutions of $g(x)=0$ is
2026-04-06 06:36:13.1775457373
How many solutions exist in reals
42 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in POLYNOMIALS
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Integral Domain and Degree of Polynomials in $R[X]$
- Can $P^3 - Q^2$ have degree 1?
- System of equations with different exponents
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Dividing a polynomial
- polynomial remainder theorem proof, is it legit?
- Polyomial function over ring GF(3)
- If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?
- $x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$
Related Questions in FACTORING
- Roots of a complex equation
- Solving for 4 variables using only 2 equations
- For any natural numbers a, b, c, d if a*b = c*d is it possible that a + b + c + d is prime number
- How can I calculate the remainder of $3^{2012}$ modulo 17?
- The complex equation $x^3 = 9 + 46i$ has a solution of the form $a + bi$ where $a,b\in \mathbb Z$. Find the value of $a^3 + b^3$
- Conversion factor
- How do I find roots of the 3rd order polynomial?
- How to find algorithm for integer factorization if the prime factorization of the integer is given?
- Define a binary operation * on the real numbers as $x * y=xy+x+y$ for all real numbers x and y.
- Computing $\lim_{x \to 1}\frac{x^\frac{1}{5}-1}{x^\frac{1}{6} -1}$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Consider $$g(x)=\frac{\alpha}{x-a}+\frac{\beta}{x-b}+\frac{\gamma}{x-c}$$ Reduce to same denominator, expand and simplify to get $$g(x)=\frac{(a b \gamma +a \beta c+\alpha b c)-x (a \beta +a \gamma +b \alpha +b \gamma + c \alpha +c \beta)+x^2 (\alpha +\beta +\gamma )}{(x-a)(x-b)(x-c)}$$
I am sure that you can take from here.