If one root of the quadratic equation `(a-b)x^2+ax+1=0` is double the other root where `a in R`, then the greatest value of b is

If one root of the quadratic equation x^2-x-1=0 is alpha the other root is

If one root of the equation (a-b) x^(2)+a x+1=0 is double the other and if a is real, then the greatest value of b is

Let alpha and beta (a lt beta) " be the roots of the equation " x^(2) + bx + c = 0," where " b gt 0 and c lt 0 . If one root of the equation (1-m) x^(2) + 1 x + 1 = 0 is double the other and 1 is real , then what is the greatest value of m?

If one root of the quadratic equation x^(2)-3x+1=0 be alpha, then its other root is given by-

If one real root of the quadratic equation 81x^2 + kx + 256=0 is cube of the other root, then a value of k is

If one real root of the quadratic equation 81x^2 + kx + 256=0 is cube of the other root, then a value of k is

If the equation ax^(2) + bx + 6 = 0 has real roots, where a in R, b in R , then the greatest value of 3a + b, is

If the equation ax^(2) + bx + 6 = 0 has real roots, where a in R, b in R , then the greatest value of 3a + b, is