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=0then h=` a.`-1/2(a/b-p/q)` b. `(b/a-q/p)` c. `1/2(b/a-q/p)` d. none of these

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

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

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

Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2beta be the roots of the equation x^2-q x+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 x^2+p x+q=0a n dgamma,delta are the roots of x^2+r x+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p ,q ,r ,a n dsdot Deduce the condition that the equation has a common root.

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

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 a. 2{p^2-2q+p^('2)-2q^(prime)-p p '} b. 2{p^2-2q+p^('2)-2q^(prime)-q q '} c. 2{p^2-2q-p^('2)-2q^(prime)-p p '} d. 2{p^2-2q-p^('2)-2q^(prime)-q q '}

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot