Pregunta
Find all other zeros of
(If there is more than one zero, separate them with commas.)
(If there is more than one zero, separate them with commas.)
Ask by Wagner Thornton. in the United States
Mar 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The other zeros are
Solución
We are given the polynomial
and one zero
Step 1. Conjugate Root Theorem
Since the polynomial has real coefficients, the complex conjugate of a zero is also a zero. Therefore,
is also a zero of
Step 2. Form the Quadratic Factor
The two complex zeros give the quadratic factor:
Rewrite each factor as:
Multiply the two factors:
Since
Expanding
thus the quadratic factor is:
Step 3. Divide the Polynomial by the Quadratic Factor
Since the polynomial is cubic, dividing by the quadratic factor
for some constant
Expanding the product:
Combine like terms:
Setting this equal to
Coefficient of
Coefficient of
which matches the coefficient
Constant term:
which matches the constant
Thus, the third zero is:
Final Answer
The other zeros of
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
To find all zeros of the polynomial
Now, let’s find the third zero. We can start by performing polynomial division to divide
Calculating the product of these factors:
This simplifies to:
Now we divide
Using synthetic or long division, we have:
where
- Divide the leading term
by to get . - Multiply
by and subtract: Now, subtract from : - Divide the leading term
by to get . - Multiply
by : Subtract this from gives .
Now we have:
To find the zeros of
Using the quadratic formula
Here,
So the zeros are
Thus, all the zeros of
preguntas relacionadas
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
