InterviewSolution
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InterviewSolution
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If `alpha` and `beta` are the roots of the equation `x^2-px + q = 0` then the value of `(alpha+beta)x -((alpha^2+beta^2)/2)x^2+((alpha^3+beta^3)/3)x^3+...` isA. `log(1+px+qx^(2))`B. `log(1+qx+px^(2))`C. `log(x^(2)+px+q)`D. none of these |
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Answer» Answer: Since `alpha,beta` are the roots of the equation `x^(2)-px+q=0` `therefore alpha+beta=p and alpha beta=q` Now `(alpha+beta)x-(alpha^(2)+beta^(2))/(2)x^(2)+(alpha^(3)+beta^(3))/(3)x^(3)`… `=((alpha x-alpha^(2))x^(2))/(2)+(alpha^(3)x^(3))/(3)+(betax-(beta^(2)x^(2))/(2)+(beta^(3)x^(3))/(3)` `=log(1+alphax)+log(1+betax)` `=log{(1+alphax)(1+betax)}` `log{(1+alpha+beta)}x+alphabetax^(2)}=log(1+px+qx^(2))` |
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