Let p and q be the roots of the quadratic equation ` x^(2) - (alpha - 2) x -alpha - 1 = 0`. What is the minimum possible value of ` p^(2) + q^(2)` ?

If p and q are the roots of the quadratic equation x^(2)+px-q=0 , then find the values of p and q.

The roots of the quadratic equation 4x^(2)-(5a+1)x+5a=0 , are p and q. if q=1+p, calculate the possible values of a,p and q.

Let p, q in R . If 2- sqrt3 is a root of the quadratic equation, x^(2)+px+q=0, then

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 ,then minimum value of alpha^(2)+beta^(2) is

Let alpha and beta be the roots of a quadratic equation 4x^(2)-(5p+1)x+5p=0. If beta=1+alpha, then the integral value of p, is

If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@) and tan15^(@) , then value of 2+q-p is

If alpha and beta are the roots of the equation x^(2) - p(x + 1) - q = 0 , then the value of : (alpha^(2) + 2 alpha + 1)/(alpha^(2)+ 2 alpha + q) + (beta^(2) + 2 beta + 1)/(beta^(2) + 2 beta + q) is :

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