Related InterviewSolutions

• Let `alpha`, `beta (a lt b)` be the roots of the equation `ax^(2)+bx+c=0`. If `lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1` thenA. `(|a|)/(a)=-1`, `m lt alpha`B. `a gt 0`, `alpha lt m lt beta`C. `(|a|)/(a)=1`, `m gt beta`D. `a lt 0`, `m gt beta`
• If `alpha, beta` are the roots of `x^(2)-3x+1=0`, then the equation whose roots are `(1/(alpha-2),1/(beta-2))` isA. `x^(2)+x-1=0`B. `x^(2)+x+1=0`C. `x^(2)-x-1=0`D. none of these
• 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 1B. `(-1/2)` and (1)C. `(-7/2)` and 2D. `(-9/2)` and 3
• 8. Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots (4,3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are:A. `-4,-3`B. `6,1`C. `4,3`D. `-6,-1`
• The number of real roots of the equation `5+|2^(x)-1|=2^(x)(2^(x)-2)is`A. 1B. 3C. 4D. 2
• The smallest value of k, for which both the roots of the equation, `x^2-8kx + 16(k^2-k + 1)=0` are real, distinct and have values at least 4, is
• Find the values of `a`for whilch the equation `sin^4x+asin^2x+1=0`will have ea solution.
• Solve the equation `2log_(3)x+log_(3)(x^(2)-3)=log_(3)0.5+5^(log_(5)(log_(3)8)`
• All the values of `m`for whilch both the roots of the equation `x^2-2m x+m^2-1=0`are greater than -2 but less than 4 lie in the interval`-23`c. `-1A. `-2 lt m lt 0 `B. `m gt 3`C. `- 1 lt m lt 3`D. `1 lt m lt 4`
• The values of x, satisfying the equation for `AA a > 0, 2log_(x) a + log_(ax) a +3log_(a^2 x)a=0` are