If `alpha and beta` be the roots of the equation `x^(2) + px - 1//(2p^(2)) = 0`,
where `p in R`. Then the minimum value of `alpha^(4) + beta^(4)` is

If alpha and beta be the roots of the eqution x^(2) +px -1/ (2p^(2)) = 0 , where p in R . Then the minimum possible value of alpha^(2) + beta^(2) is

If alpha and beta are the roots of the equation x^(2)+px-(1)/(2p^(2))=0, where p in R .Then,the minimum value of alpha^(4)+beta^(4) is

If alpha, and beta be t roots of the equation x^(2)+px-1/2p^(2)=0, where p in R. Then the minimum value of alpha^(4)+beta^(4) is 2sqrt(2) b.2-sqrt(2)c2d.2+sqrt(2)

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

If alpha and beta are the real roots of the equation x^(3)-px-4=0, p in R such that 2 alpha+beta=0 then the value of (2 alpha^(3)+beta^(3)) equals

If alpha and beta are are the real roots of the equation x^(3)-px-4=0,p in R such that 2alpha+beta=0 then the value of (2alpha^(3)+beta^(3)) equals

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

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :