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

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

If the roots of the equation x^(2)-lx+m=0 differ by 1, then

If the roots of the equation px^(2)+qx+r=0 are in the ratio l:m then

If roots of the equation lx^(2)+mx-2=0 are real and reciprocal of each other,then

If one root of the equation lx^2+mx+n=0 is 9/2 (l, m and n are positive integers) and m/(4n)=l/m , then l+ n is equal to :