If one root of equation `(l-m) x^2 + lx + 1` = 0 be double of the other and if `l` be real, show that `m<=9/8`

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 equation (l-m)x^(2)+lx+1=0 is double the other and l is a real number, then which of the following is true ?

If one roots of the equation x^(2) - mx + n = 0 is twice the other root, then show that 2m^(2) = 9pi .

If for all real values of a one root of the equation x^(2)-3ax+f(a)=0 is double of the other,then f(x) is equal to

If the roots of the equation lx^(2) +mx +m=0 are in the ratio p:q, then

If one root of the equation (x-1)(7-x)=m is three xx the other, then m is equal to

If one root of the equation (x-1)(7-x)=m is three times the other, then m is equal to

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