The problem involves finding the value of 'a' for which the polynomial equations x³ + ax + 1 = 0 and x⁴ + ax + 1 = 0 share a common root. Participants are exploring the implications of this shared root in the context of polynomial equations.
The discussion is ongoing, with participants sharing their attempts and questioning the accuracy of the provided answer. Some guidance has been offered regarding the need to verify assumptions and seek consensus on the findings.
There is a noted discrepancy between the calculated value of 'a' (-2) and the answer given in the problem (-1), leading to further questioning of the assumptions and methods used in the calculations.
Please show how you did it, and why it did not work.vijayramakrishnan said:Homework Statement
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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 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 sirSamy_A said:Please show how you did it, and why it did not work.
What you write seems to be the way to go.
a = -2 : looks correct to me.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.
than you sir for replyingSamy_A said:a = -2 : looks correct to me.
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 said:than you sir for replying
then answer must be wrong,sorry for wasting your time
yes sir thank you very muchSamy_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.