[" 3.(i) "2 pi" ,"2" ,r "8" (arss ismes "B" ar "2" ? "],[[1,(2)/(p)quad alpha+(2)/(p)|],[1,(r)/(2)quad alpha+(r)/(2)|=0" ?? "],[p alpha+2," qatr "0]]

If p, q, r are not in G.P. and |[1,q/p,alpha+q/p],[1,r/p,alpha+r/q],[palpha+q,qalpha+r,0]|=0 Show that palpha^2+2qalpha+r=0

If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),(palpha+q,qalpha+r,0)|=0 then prove that palpha^2+2qalpha+r=0

If p,q,r are not in geometric progression and |[1,q/p,alpha+q/p],[1,r/q,alpha+r/q],[palpha+q,qalpha+r,0]|=0 then prove that palpha^2+2q alpha^2+r=0

a in R and (alpha-2)x^(2)+8x+alpha+4<0,AA x in R, then alpha cannot be

If alpha, beta , gamma are the roots of x^(3) - px^(2) + qx - r = 0 then match the following. (1)/(alpha) + (1)/(beta) + (1)/(gamma)" "(a)(p^(2) - 2q)/(r^(2)) ii. (1)/(alpha beta) + (1)/(beta gamma) + (1)/(gamma alpha)=" "(b) (q^(2) - 2pr)/(r^(2)) iii. (1)/(a^(2)) + (1)/(beta^(2)) + (1)/(gamma^(2)) =" " (c ) (p)/(r ) iv. (1)/(alpha^(2) beta^(2)) + (1)/(beta^(2) gamma^(2) ) + (1)/(gamma^(2) alpha^(2)) = " " (d) (q)/(r )

Let P=[(3,-1,-2),(2,0,alpha),(3,-5,0)] , where alpha in R . Suppose Q =[q_(ij)] is a matrix satisfying PQ = KI_3 for some non - zero K in R . If q_(23) =- (K)/(8) and |Q| = (1)/(2), then alpha^2 + k^2 is equal to ________.

If the line x cos alpha+y sin alpha=p touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ,then the point of contact will be ((-a^(2)cos alpha)/(p),(-b^(2)sin alpha)/(p)) ((b^(2)cos alpha)/(p),(a^(2)sin alpha)/(p)) ((b^(2)sin alpha)/(p),(a^(2)cos alpha)/(p)) ( (a^(2)cos alpha)/(p),(b^(2)sin alpha)/(p))