`2 x^2-(2 a+1)2 x+a(a-1)=0 ` has roots `alpha and beta ` satisfying `alpha < a < beta, then a in.`

If x^(2)+(a^(2)+100)x-2a=0 (where a in R) has the roots alpha and beta, then minimum value of (1-alpha)(1-beta) is

If alpha and beta are roots of the equation x^2 – x-1 = 0 , then the equation where roots are alpha/beta and beta/alpha is:

IF alpha and beta be the roots of the equation 2x^2+x+1=0 find the equation whose roots are alpha^2/beta and beta^2/alpha

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. If alpha and beta are the roots of the equation 1+x+x^(2) = 0 , then the matrix product [{:(1,beta),(alpha,alpha):}],[{:(alpha,beta),(1,beta):}] is equal to

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. If alpha and beta are the roots of the equation 3x^(2) + 2 x + 1 = 0 , then the equation whose roots are alpha + beta ^(-1) and beta + alpha ^(-1)

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 and beta are the roots of 2x^2-5x+3=0 form the equation whose roots are alpha+beta and 1/alpha+1/beta

2x^2+3x-1=0 is a quadratic equation the roots are alpha,beta then alpha^2+beta^2 =……….

If alpha, beta are the roots of x^(2)+2x-1=0 , then the equation whose roots are alpha^(2), beta^(2) is