If the roots of `ax^2+2bx+c=0` be possible and different then prove that the roots of `(a+c)(ax^2+2bx+2c) = 2 (ac-b^2)(x^2+1)` will be impossible

If the roots of ax^2+2bx+c=0 be possible and different then show that the roots of (a+c)(ax^2+2bx+2c)=2(ac-b^2)(x^2+1) will be impossible and vice versa

Prove that the roots of ax^2+2bx+c=0 will be real and distinct if and only if the roots of (a+c) (ax^2+2bx+c) =2 (ac-b^2) (x^2+1) are imaginary

Prove that the roots of ax^(2)+2bx + c = 0 will be real distinct if and only if the roots of (a+c)(ax^(2)+2bx + c)=2(ac-.b^(2))(x^(2)+1) are imaginary.

Sum of the roots of ax^(2) + bx + c = 0 is..

Product of the roots of ax^(2) + bx + c = 0 is…

Sum of the roots of bx^(2) + ax + c = 0 is

If the roots of the equation ax^2 + bx + c = 0 are in the ratio 2:3 , then prove that 6b^2 = 25ac

If the roots of the equation ax^2+bx+c=0 are two consecutive integers then prove that, b^2-a^2=4ac .

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 differ by K then b^(2)-4ac=