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| 1. |
If f(x) = x3 + x2 - ax + b is divisible by x2 -x write the value of a and b |
| Answer» Since f(x) =\xa0x3\xa0+ x2\xa0- ax + b is divisible by (x2\xa0- x), we havex2\xa0- x = 0{tex}\\Rightarrow{/tex}\xa0x(x - 1) = 0{tex}\\Rightarrow{/tex}\xa0x = 0 or x = 1Hence,f(0) = 0{tex}\\Rightarrow{/tex} x3\xa0+ x2\xa0- ax + b = 0{tex}\\Rightarrow{/tex}\xa003\xa0+ 02\xa0- a(0) + b = 0{tex}\\Rightarrow{/tex}\xa0b = 0Also,f(1) = 0{tex}\\Rightarrow{/tex} x3\xa0+ x2\xa0- ax + b = 0{tex}\\Rightarrow{/tex}\xa013\xa0+ 12\xa0- a(1) + 0 = 0{tex}\\Rightarrow{/tex}\xa01 + 1 - a = 0{tex}\\Rightarrow{/tex} 2 - a = 0{tex}\\Rightarrow{/tex}\xa0a = 2Hence , the value of a and b in given polynomial are a = 2 and b = 0. | |