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(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) 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(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

If alpha and beta are the roots of the equation 3x^(2)+8x+2=0 then ((1)/(alpha)+(1)/(beta))=?

If alpha and beta are the roots of the equation 4x^(2)+3x+7=0, then (1)/(alpha)+(1)/(beta)=

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:

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