InterviewSolution
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InterviewSolution
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Find the value of k, if x-1 is a factor of p(x) in each of the following cases : (i) `p(x)=x^(2)+x+k " " (ii) p(x)=2x^(2)+kx+sqrt(2)` (iii) `p(x)=kx^(2)-sqrt(2)x+1 " " (iv) p(x) =kx^(2)-3x+k` |
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Answer» The zero of x-1 is 1. (i) `because (x-1)` is a factor of p(x), then p(1)=0 `implies 1^(2)+1+k=0 " " [because p(x)=x^(2)+x+k]` `implies 2+k=0` `implies k=-2` (ii) `because (x-1)` is a factor of p(x), then p(1)=0 `implies 2(1)^(2)+k(1)+sqrt(2)=0 " " [because p(x)=2x^(2)+kx+sqrt(2)]` `implies 2+k+sqrt(2)=0` `implies k=-(2+sqrt(2))` (iii) `because (x-1)` is a factor of p(x), then p(1)=0 `implies k(1)^(2)-sqrt(2)+1=0 " " [because p(x)=kx^(2)-sqrt(2)+1]` `implies k=(sqrt(2)-1)` (iv) `because (x-1)` is a factor of p(x), then p(1)=0 `implies k(1)^(2)-3+k=0 " " [because p(x)=kx^(2)-3x+k]` `implies 2k-3=0` `implies k=(3)/(2)` |
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