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CONSIDER THE EQUATION x^5 + x= 10. SHOW THAT THE EQUATION HAS ONLY ONE REAL ROOT; ALSO THAT THE ROOT LIES BETWEEN 1 AND 2; AND ALSO THAT THE ROOT MUST BE IRRATIONAL.

CONSIDER THE EQUATION x^5 + x= 10.  SHOW THAT THE EQUATION HAS ONLY ONE REAL ROOT; ALSO THAT THE ROOT LIES BETWEEN 1 AND 2; AND ALSO THAT THE ROOT MUST BE IRRATIONAL.

Grade:11

1 Answers

jitender lakhanpal
62 Points
10 years ago

Dear Aritra,

 

   f(x)=   x^5 + x - 10 = 0 

number of times the sign changes in the expression is 1 so it can have utmost 1 real root 

and now put x = 1 we get f(1) = -8   so <0

and if we put x = 2  we get f(2) = 24  so >0

so we see that there will be root between 1 and 2

 

 

 

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