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

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 .

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 a,b,c are in G.P prove that the roots of the equation ax^2+2bx+c=0 are equal.

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

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

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 roots of the equation ax^(2)+2(a+b)x+(a+2b+c)=0 are imaginary then roots of the equation ax^(2)+2bx+c=0 are

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

If a and c are the lengths of segments of any focal chord of the parabola y^(2)=bx,(b>0) then the roots of the equation ax^(2)+bx+c=0 are real and distinct (b) real and equal imaginary (d) none of these