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

[vijayramakrishnan]

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.

 

[Samy_A]

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.

 

[vijayramakrishnan]

Please show how you did it, and why it did not work.
What you write seems to be the way to go.

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.

 

[Samy_A]

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.

 

[vijayramakrishnan]

a = -2 : looks correct to me.

than you sir for replying
then answer must be wrong,sorry for wasting your time

 

[Samy_A]

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.

 

[vijayramakrishnan]

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