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

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

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 (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

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

Let a,b,c , d ar positive real number such that a/b ne c/d, then the roots of the equation: (a^(2) +b^(2)) x ^(2) +2x (ac+ bd) + (c^(2) +d^(2))=0 are :

Check that if the roots of the equation (a^2+b^2)x^2+2x(ac+bd)+c^2+d^2=0 are real,whether they will be equal

If a,b,c,d, x are real and the roots of equation (a^2+b^2+c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2)=0 are real and equal then a,b,c,d are in (A) A.P (B) G.P. (C) H.P. (D) none of these

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 (a^2+b^2)x^2-2(a c+b d)x+c^2+d^2=0 has equal roots, then (a) a b=c d (b) a d=b c (c) a d=sqrt(b c) (d) a b=sqrt(c d)

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.