If roots `alpha` and `beta` of the equation `x^2+px+q =0` are such that `3 alpha +4beta =7` and `5alpha -beta = 4` then (p,q) is equal to

Let alpha and beta be the roots of the equation px^(2) + qx + r=0 . If p, q, r in AP and alpha+beta =4 , then alpha beta is equal to

If alpha and beta are the roots of the equation x^(2) + px + q =0, then what is alpha ^(2) + beta ^(2) equal to ?

Let alpha" and "beta be the roots of the equation px^(2)+qx+r=0 . If p,q, r in A.P. and alpha+beta=4 , then alpha beta is equal to

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

If alpha and beta are roots of the equation qx^2+px+p=0 ,show that sqrt(alpha/beta)+sqrt(beta/alpha)+sqrt(p/q)=0

If the roots of the equation x^(2)-5x+16=0 are alpha and beta and the roots of the equation x^(2)+px+q=0 are alpha^(2)+beta^(2) and (alpha beta)/(2), then

IF alpha and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .

If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is