What is the common root for two polynomial equations with a shared coefficient?

In summary, the conversation discusses finding the value of 'a' that will satisfy the equations x3+ax+1=0 and x4+ax+1=0 having a common root. The attempt at a solution involves subtracting the two equations and finding possible values for x, but the answer given (-1) does not match the result obtained (-2). After discussing with the expert, it is determined that the given answer may be incorrect.
  • #1
vijayramakrishnan
90
0

Homework Statement


[/B]
Th value of 'a' for which the equation x3+ax+1=0 and x4+ax+1=0 have a common root is?

Homework Equations

The Attempt at a Solution



i initially thought of subtracting both the equations and then finding x and substituting back in the equation but it did not work.
 
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  • #2
vijayramakrishnan said:

Homework Statement


[/B]
Th value of 'a' for which the equation x3+ax+1=0 and x4+ax+1=0 have a common root is?

Homework Equations

The Attempt at a Solution



i initially thought of subtracting both the equations and then finding x and substituting back in the equation but it did not work.
Please show how you did it, and why it did not work.
What you write seems to be the way to go.
 
  • #3
Samy_A said:
Please show how you did it, and why it did not work.
What you write seems to be the way to go.
Samy_A said:
Please show how you did it, and why it did not work.
What you write seems to be the way to go.
thank you for replying sir
subtracting we get x4-x3=0
x can be 1 or 0.
substituting back in the equation we get a = -2
but answer given is -1.
 
  • #4
vijayramakrishnan said:
thank you for replying sir
subtracting we get x4-x3=0
x can be 1 or 0.
substituting back in the equation we get a = -2
but answer given is -1.
a = -2 : looks correct to me.
 
  • #5
Samy_A said:
a = -2 : looks correct to me.
than you sir for replying
then answer must be wrong,sorry for wasting your time
 
  • #6
vijayramakrishnan said:
than you sir for replying
then answer must be wrong,sorry for wasting your time
No need to apologize: when a given answer looks wrong (something that can happen), the best you can do is ask to see if others agree.
 
  • #7
Samy_A said:
No need to apologize: when a given answer looks wrong (something that can happen), the best you can do is ask to see if others agree.
yes sir thank you very much
 

1. What is a polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, combined using operations such as addition, subtraction, multiplication, and exponentiation. It can have one or more terms, with each term containing a variable raised to a non-negative integer power.

2. What is the degree of a polynomial?

The degree of a polynomial is the highest exponent of the variable in the expression. For example, in the polynomial 3x^2 + 5x + 2, the degree is 2.

3. How do you solve a problem from polynomials?

To solve a problem from polynomials, you can use various techniques such as factoring, the quadratic formula, or the remainder theorem. The specific method will depend on the type of problem and the level of complexity.

4. What are some real-life applications of polynomials?

Polynomials have many real-life applications, including in physics, engineering, and economics. They are used to model and analyze various phenomena, such as motion, growth, and optimization problems.

5. Can polynomials have imaginary or complex roots?

Yes, polynomials can have imaginary or complex roots. This means that the solutions to the polynomial equation may involve complex numbers, which have both a real and imaginary part. In some cases, the polynomial can be factored into linear and quadratic factors that can then be solved using the quadratic formula.

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