If `a,b,c`are +ve and `a=2b+3c` ,then roots of the equation `ax^(2)+bx+c=0`are real for

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for

If a, b and c are positive real and a = 2b + 3c , then the equation ax^(2) + bx + c = 0 has real roots for

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0

If sin theta, cos theta are the roots of the equation ax^(2)+bx+c=0 then find the value of ((a+c)^(2))/(b^(2)+c^(2))

Statement -1 : if a,b,c not all equal and a ne 0 ,a^(3) +b^(3) +c^(3) =3abc ,then the equation ax^(2) +bx+c=0 has two real roots of opposite sign. and Statement -2 : If roots of a quadractic equation ax^(2) +bx +c=0 are real and of opposite sign then ac lt0.

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

Let alpha , beta (a lt b) be the roots of the equation ax^(2)+bx+c=0 . If lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1 then