If `ax^(2)+bx+c=0, a,b, c in R`, then find the condition that this equation would have atleast one root in (0, 1).

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

Consider a quadratic equation az^2+bz+c=0, where a,b and c are complex numbers. The condition that the equation has one purely real root, is

The equation ax^(2) +bx+ c=0, where a,b,c are the side of a DeltaABC, and the equation x^(2) +sqrt2x+1=0 have a common root. Find measure for angle C.

a, b, c in R, a!= 0 and the quadratic equation ax^2+bx+c=0 has no real roots, then

If |ax^2 + bx+c|<=1 for all x is [0, 1] ,then

Find the conditions if roots of the equation x^(3)-px^(2)+qx-r=0 are in (i) AP

If ax^(2)+bx+c=0 have two distinct roots lying in the interval (0,1),a,b,c \in N The least value of b is

If ax^2-bx + c=0 have two distinct roots lying in the interval (0,1); a, b,in N , then the least value of a , is

If ax^(2)-bx+5=0 does not have two distinct real roots, then find the minimun value of 5a+b.

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in