`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.`
It is given that the roots of the equation `x^(2) - 4x - log_(3) P=0` are real . For this, the minimum value of P is

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. The roots of the equation (q-r)x^(2)+ ( r-p)x + (p-q) = 0 are

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. The sum of all real roots of the equation |x-3|^(2) +|x-3|-2 = 0 is

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. The equation |1-x|+ x^(2) = 5 has

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 beta,2,2m are in GP, then what is the value of beta sqrt(m) ?

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 cot alpha and cot beta are the roots of the equation x^(2)+ bx + c = 0" with " b != 0, " then the value of " cot(alpha + beta) is

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)

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 the roots of the equation x^(2) + px+ q = 0 are in the same ratio as those of the equation x^(2) +lx + m = 0 , then which one of the following is correct ?

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. Let [x] denote the greatest integar function. What is the number of solutions of the equation x^(2) - 4x+ [x] - 0 " in the interval " [0,2] ?

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. Delta PQR, angleR=pi/2. " If than "(P/2) and tan (Q/2) " are the roots of the equation " ax^(2) + bx + c = 0 , then which one of the following is correct ?

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