If $\alpha ,\beta$ are the roots of $x^2 -ax + b = 0$ and if $\alpha^n + \beta^n = V_n$, then -
$V_{n+1} = aV_n + bV_{n-1}$
$V_{n+1} = aV_n + aV_{n-1}$
$V_{n+1} = aV_n -bV_{n-1}$
$V_{n+1} = aV_{n-1} -bV_n$
The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is
For what value of $\lambda$ the sum of the squares of the roots of ${x^2} + (2 + \lambda )\,x - \frac{1}{2}(1 + \lambda ) = 0$ is minimum
Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to
The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is
If $\alpha, \beta $ and $\gamma$ are the roots of the equation $2{x^3} - 3{x^2} + 6x + 1 = 0$, then ${\alpha ^2} + {\beta ^2} + {\gamma ^2}$ is equal to