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10th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If p, q are the zeroes of the polynomial \[f(x)={{x}^{2}}+k(x-1)-c,\] then \[(p-1)\,(q-1)\]is equal to _____.

    A)  \[c-1\]                         

    B)  \[1-c\] 

    C)         c                    

    D)         \[1+c\]                       

    Correct Answer: B

    Solution :

    Given equation is \[{{x}^{2}}+k(x-1)-c\] \[={{x}^{2}}+kx-(k+c)\]             Since, p and q are the zeroes,             \[\therefore \]   \[p+q=-k\] and \[pq=-(k+c)\]             Now, \[(p-1)(q-1)=pq-q-p+1\]             \[=pq-(p+q)+1=-(k+c)-(-k)+1\]             \[=-k-c+k+1=1-c\]


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