If the polynomial x^3+2x^2+ax+b has factors …
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Posted by Ronak Gupta 8 years, 5 months ago
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Payal Singh 8 years, 5 months ago
p(x) = {tex}x^3+2x^2+ax+b{/tex}
As x+1 is factor of p(x)
Then
p(-1)=0
=> {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
=> {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 =-2
From (2)
=> 2+a=-3
=> a = -5
0Thank You