Let `a, b, c gt 0`. Then prove that both the roots of the equation
`ax^(2)+bx+c=0` has negative real parts.

If the roots of the equation x^(2) - bx + c = 0 are two consecutive integers, then b^(2) - 4c is

If sin alpha and cos alpha are the roots of the equition ax^(2) + bx + c = 0 , then

If c, d are the roots of the equation (x-a) (x-b) - k=0 , then prove that a, b are the roots of the equation (x-c) (x-d) + k= 0

If alpha and beta are the roots of the equation ax^(2) + bx + c = 0, (c ne 0) , then the equation whose roots are (1)/(a alpha +b) and (1)/(a beta + b) is