Prove that the roots of equation `bx^2+(b-c)x+b-c-a=0` are real if those of equatiion `ax^2+2bx+b=0` are imaginary and vice versa where `a,b,c epsilon R`.

If the ratio of the roots of the equation ax^2+bx+c=0 is equal to ratio of roots of the equation x^2+x+1=0 then a,b,c are in

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

If the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are real numbers), are imaginary and a + c < b, then

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

The expression ax^2+2bx+b has same sign as that of b for every real x, then the roots of equation bx^2+(b-c)x+b-c-a=0 are (A) real and equal (B) real and unequal (C) imaginary (D) none of these

If 0 lt c lt b lt a and the roots alpha, beta the equation cx^(2)+bx+a=0 are imaginary, then

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real roots, then

If b^(2)ge4ac for the equation ax^(4)+bx^(2)+c=0 then all the roots of the equation will be real if