If a ,b ,c are non zero rational no then prove roots of equation `(a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0` are rational.

If a ,b ,c are non zero (a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 are rational.

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in R

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

Let a , ba n dc be the three sides of a triangle, then prove that the equation b^2x^2+(b^2=c^2-alpha^2)x+c^2=0 has imaginary roots.

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot