Let `alpha(p) and beta(p)` be the roots of the equation `(root(6)(1+p)-1)x^2 +(root(3)(1+p)+1)x+(root(9)(1+p) - 1) = 0` where `pgt-1` then `lim_(p rarr 0^+) [alpha(p)+ beta(p)]` is equal to

Let alpha(p) and beta(p) be the roots of the equation (root(6)(1+p)-1)x^(2)+(root(3)(1+p)+1)x+(root(9)(1+p)-1)=0 where p>-1 then lim_(p rarr0^(+))[alpha(p)+beta(p)] is equal to

Let alpha (a) beta (a) be the roots of the equations : (root(3)(1+a) -1)x^(2) + (sqrt(1 + a) - 1)x + (root(6)(1 + a) - 1) = 0 , where a gt - 1 . Then lim_(a rarr 0^(+)) alpha (a) and lim_(a rarr 0^(+)) beta(a) are :

Let alpha(a) and beta(b) be the roots of the equation , (root(3)(1+a)-1)x^2+(sqrt(1+a)-1)x+(root(6)(1+a)-1)=0 where a gt -1 . Then lim_(x rarr 0^+)alpha(a) and lim_(x rarr 0^+) beta(a) are

If alphaandbeta be the roots of the equation x^(2)-px+q=0 then, (alpha^(-1)+beta^(-1))=(p)/(q) .

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If alpha and beta are the roots of the equations x^2-p(x+1)-c=0 , then (alpha+1)(beta+1)_ is equal to: