If a root of the given equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$ is $1$,then the other root will be

Let $\lambda \neq 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+2\lambda=0$ and $\alpha$ and $\gamma$ are the roots of the equation $3x^{2}-10x+27\lambda=0$,then $\frac{\beta\gamma}{\lambda}$ is equal to

If $A.M.$ and $G.M.$ of roots of a quadratic equation are $8$ and $5,$ respectively,then obtain the quadratic equation.

The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is

If the roots of the equation $ax^2 + bx + c = 0$ are $l$ and $2l$,then

If $\alpha, \beta$ are the roots of $x^2+ax+2=0$ and $\frac{1}{\alpha}, \frac{1}{\beta}$ are the roots of $x^2-bx+c=0$,then $\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right) = $