If `alpha,beta` are the roots of `a x^2+b x+c=0a n dalpha+h ,beta+h` are the roots of `p x^2+q x+r=0t h e nh=` `-1/2(a/b-p/q)` b. `(b/a-q/p)` c. `1/2(b/q-q/p)` d. none of these

If alpha,beta are roots of x^(2)-px+q=0 and alpha-2,beta+2 are roots of x^(2)-px+r=0 then prove that 16q+(r+4-q)^(2)=4p^(2)

If a,b are the roots of x^(2)+px+1=0 and c d are the roots of x^(2)+qx+1=0, Then ((a-c)(b-c)(a+d)(b+d))/(q^(2)-p^(2))

If alpha,beta are the roots of x^(2)+px+q=0and gamma,delta are the roots of x^(2)+px+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= a.1b.q c.r d.q+r

If alpha,beta are the nonzero roots of ax^(2)+bx+c=0 and alpha^(2),beta^(2) are the roots of a^(2)x^(2)+b^(2)x^(2)+b^(2)x+c^(2)=0, then a,b,c are in a.G.P.b.H.P. C.A.P.d.none of these

If alpha,beta are roots of the equation (3x+2)^(2)+p(3x+2)+q=0 then roots of x^(2)+px+q=0 are

If alpha,beta are the roots of x^2-p x+q=0a n dalpha^(prime),beta' are the roots of x^2-p^(prime)x+q^(prime)=0, then the value of (alpha-alpha^(prime))^2+(beta-alpha^(prime))^2+(alpha-beta^(prime))^2+(beta-beta^(prime))^2 is 2{p^2-2q+p^('2)-2q^(prime)-p p '} 2{p^2-2q+p^('2)-2q^(prime)-q q '} 2{p^2-2q-p^('2)-2q^(prime)-p p '} 2{p^2-2q-p^('2)-2q^(prime)-q q '}

If alpha,beta are the roots of the equation x^(2)+px-r=0 and (alpha)/(3),3 beta are the roots of the equation x^(2)+qx-r=0, then r equals (i)((3)/(8))(p-3q)(3p+q)(ii)((3)/(8))(3p-q)(3p+q)(iii)((3)/(64))(q-3p)(p-3p)(iv)((3)/(64))(p-q)(q-3p)

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha/2,2 beta be the roots of the equation x^(2)-qx+r=0. Then the value of r is (2)/(9)(p-q)(2q-p) b.(2)/(9)(q-p)(2q-p) c.(2)/(9)(q-2p)(2q-p) d.(2)/(9)(2p-q)(2q-p)

If alpha, beta are the roots of the equations x^2+px+q=0 then one of the roots of the equation qx^2-(p^2-2q)x+q=0 is (A) 0 (B) 1 (C) alpha/beta (D) alpha beta