If `a^2x^2+b x+c=0` has roots `alpha&beta(alpha

lf a^2x^2 + bx + c =0 has roots alpha and beta(alpha lt beta) and -p^2x^2 + qx + r = 0 has roots alpha+ 5 and beta-5 then (a^2+ p^2)x^2 + (b-q)x + (c-r) = 0 has a root in interval (given alpha+5 lt beta -5 )

If 2x^(3) + 3x^(2) + 5x +6=0 has roots alpha, beta, gamma then find alpha + beta + gamma, alphabeta + betagamma + gammaalpha and alpha beta gamma

The quadratic equation x^(2)-9x+3=0 has roots alpha and beta.If x^(2)-bx-c=0 has roots alpha^(2)and beta^(2), then (b,c) is

If (x + 2)(x + 3b) = c has roots alpha,beta , then the roots of (x + alpha)(x+beta) + c = 0 are

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

Let alpha,beta be the roots of the equation ax^2+bx+c=0 . A root of the equation a^3x^2+abcx+c^3=0 is (i) alpha+beta (ii) alpha^2+beta (iii) alpha^2-beta (iv) alpha^2beta

If alpha,beta re the roots of a x^2+c=b x , then the equation (a+c y)^2=b^2y in y has the roots a. alphabeta^(-1),alpha^(-1)beta b. alpha^(-2),beta^(-2) c. alpha^(-1),beta^(-1) d. alpha^2,beta^2

If alpha&beta are the roots of the quadratic equation a x^2+b x+c=0 , then the quadratic equation, a x^2-b x(x-1)+c(x-1)^2=0 has roots: alpha/(1-alpha),beta/(1-beta) (b) alpha-1,beta-1 alpha/(alpha+1),beta/(beta+1) (d) (1-alpha)/alpha,(1-beta)/beta

If alpha, beta and gamma are the roots of the equation x^(3)+x+2=0 , then the equation whose roots are (alpha- beta)(alpha-gamma), (beta-gamma)(beta-gamma) and (gamma-alpha)(gamma-alpha) is

If the roots of a_1x^2 + b_1x+ c_1 = 0 are alpha_1 ,beta_ 1 and those of a_2x^2+b_2x+c_2=0 are alpha_2,beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then