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Perfect square

  • Thread starter ritwik06
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1. Homework Statement

If the polynomial P(x)=x^4+ax^3+bx^2-8x+1 is a perfect square then find (a+b)

3. The Attempt at a Solution
The first term is a perfect square and so is the last term. that means that th middle terms should have been =2x^2.
But it is not so, then how can this be a perfect square?
 

Answers and Replies

HallsofIvy
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P(x) is a perfect square of what? Since it involves x4, it must be the square of a quadratic. What is (x^2+ ux+ 1)2? What values of a, b, and u make those the same?
 
Last edited by a moderator:
580
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P(x) is a perfect square of what? Since it involves x4[/itex], it must be the square of a quadratic. What is (x^2+ ux+ 1)2? What values of a, b, and u make those the same?


Thanks. I have solved the problem. But will you please tell me how did you figure out that the skeleton expression given was the square of a trinomial?
 
HallsofIvy
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I didn't "figure" that out. The given expression involved x4 so I knew it must be the square of a quadratic. The most general quadratic is ax2+ bx+ c. Then I saw that, in order to get "x4" and "+ 1" I must have a= 1, c= 1. I still did not know what b was so I left that in. I did not know that b was not 0, just that there was no reason to assume it wasn't!
 

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