If `alpha` is the only real root of the equation `x^3+px^2-qx+1=0` and `p+q <0`. Then ` |[tan^(-1)a + tan^(-1)(a^(-1))]|` ...where [ . ] is the greatest integer function.

If alpha,beta,gamma are the real roots of the equation,x^(3)-3px^(2)+3qx-1=0, the cetroid of the triangle whose vertices are (alpha,(1)/(alpha)),(beta,(1)/(beta)),(gamma,(1)/(gamma)) is: a.(p,p) b.(p,0) c.(p,q) d.(q,0)

If alpha,beta,gamma are the real roots of the equation,x^(3)-3px^(2)+3qx-1=0, the centroid of the triangle whose vertices are (alpha,(1)/(alpha)),(beta,(1)/(beta)),(gamma,(1)/(gamma))quad is(p,p)(b)(p,0)(p,q)(d)(q,0)

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum (1)/(alpha beta ) =

If alpha, beta, gamma are roots of the equation x^(3)+px^(2)+qx+r= 0 , then prove that (1-alpha^(2))(1- beta^(2)) (1- gamma^(2))=(1+q)^(2)-(p+r)^(2)

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum(alpha - beta )^(2) =

If alpha, beta, gamma are roots of the equation x^(3) - px^(2) + qx - r = 0 , then sum alpha^(2) beta =

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the cquation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is

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