Related InterviewSolutions

• cIf `a_1,a_2,a_3,..,a_n in R` then `(x-a_1)^2+(x-a_2)^2+....+(x-a_n)^2` assumes its least value at x=A. `a_(1) + a_(2) +....+a_(n)`B. `2(a_(1) + a_(2), a_(3) +....+a_(n))`C. `n(a_(1)+a_(2)+....+a_(n))`D. none of these
• If `alpha` and `beta` are the roots of the equation `x^2-ax+b=0` and `A_n=alpha^n+beta^n`,A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.
• lf `alpha and beta` are the roots of the equation `x^2-ax + b = 0 and A_n = alpha^n + beta^n`, then which of the following is true ?A. `A_(n+1) = a A_(n) + b A_(n-1)`B. `A_(n+1) = b A_(n) + a A_(n-1)`C. `A_(n+1) = a A_(n) - b A_(n-1)`D. `A_(n+1) = b A_(n) - a A_(n-1)`
• let `alpha(a)` and `beta(a)` be the roots of the equation `((1+a)^(1/3)-1)x^2 +((1+a)^(1/2)-1)x+((1+a)^(1/6)-1)=0` where `agt-1` then, `lim_(a->0^+)alpha(a)` and `lim_(a->0^+)beta(a)`A. `-(5)/(2) and 1`B. `-(1)/(2) and -1`C. `-(7)/(2) and 2`D. `-(9)/(2) and 3`
• The roots of the equation `3x^(2) - 4sqrt(3x) + 4 = 0` are
• If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.
• The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.
• The number of distinct real solution of `|x|^(2) - 5|x| + 6 = 0` isA. 4B. 3C. 2D. 1
• If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.
• Which of the following equations has roots as a,b and c ?A. `x^(3) + x^(2)(a+b+c) + x(ab+bc+ca) + abc = 0`B. `x^(3)+x^(2)(a+b+c)+x(ab+bc+ca) - abc = 0`C. `x^(3) - x^(2)(a+b+c) + x(ab+bc+ca)-abc = 0`D. `x^(3)-x^(2)(a+b+c)-x(ab+bc+ca) - abc = 0`