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| 1. |
If the polynomial x^3+2x^2+ax+b has factors x+1 and x-1, find the value of a and b |
| Answer» p(x) =\xa0{tex}x^3+2x^2+ax+b{/tex}As x+1 is factor of p(x)Thenp(-1)=0=>\xa0{tex}(-1)^3+2(-1)^2+a(-1)+b=0{/tex}{tex}=>-1+2-a+b=0{/tex}=> b-a = -1 .......(1)Also x-1 is factor of p(x)p(1)=0=>\xa0{tex}(1)^3+2(1)^2+a(1)+b=0{/tex}=> 1+2+a+b=0=> b+a=-3 .......(2)Adding (1) and (2), we get=> 2b= -4=> b =-2From (2)=> 2+a=-3=> a = -5\xa0 | |