`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. 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. 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. 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 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 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. 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. 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. 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 omega, omega^(2) are the cube roots of unity, then (1+omega) (1+omega^(2))(1+omega^(3)) (1+ omega + omega ^(2)) 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 the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct ?