The discussion centers on determining the value of 'a' for which the polynomial equations x3 + ax + 1 = 0 and x4 + ax + 1 = 0 share a common root. The initial approach involved subtracting the two equations, leading to x4 - x3 = 0, which yields potential roots of x = 1 or x = 0. Substituting these values back into the original equations resulted in a = -2, although the expected answer was -1, prompting further discussion on the correctness of the provided solution.
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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.