Let `alpha (a) and beta (a)` be the roots of the equation `(3sqrt(1+ a)-1) x^2- (sqrt1 + a) -1) x+ (6sqrt(1 + a) -1) =0`, wherea `a>-1`. Then, `lim_(alpha->0^+) beta (a) and lim_(alpha->o^+) beta (a)` are

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

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)

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)

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)

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) 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 a>-1 then,lim_(a rarr0^(+))alpha(a) and lim_(a rarr0^(+))beta(a)

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta be the roots of the equation x^2-1=0 , then show that. alpha+beta=(1)/(alpha)+(1)/(beta)