If `a,b, cinR`, show that roots of the equation `(a-b)x^(2)+(b+c-a)x-c=0` are real and unequal,

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

6.The roots of the equation (a-b+c)x^(2)+4(a-b)x+(a-b-c)=0 are

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

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

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

If the roots of the equation , x^2+2c x+ab=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

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

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