If the roots of the equation `(c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0` are equal, prove that either `a=0` or `a^3+b^3+c^3=3a b cdot`

If the roots of the equation (c^(2)-ab)x^(3)-2(a^(2)-bc)x+b^(2)-ac=0 are real and equal prove that either a=0 (or) a^(3)+b^(3)+c^(3)=3"abc" .

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1//c dot

If the equation (b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0 has equal roots, then

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are equal, prove that 2a=b+c .

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

If roots of equation x^2+2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

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 the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common root then prove that either b+c+1=0 or b^2+c^2+1=bc+b+c .