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.
Dear Aritra,
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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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