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

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 the roots of the equation : a(b - c)x^2 +b (c - a)x + c(a - b) = 0 are equal, show that 1/a,1/b,1/c are in A.P.

If a,b,c are in A.P. then :

If a, b,c be the sides of a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=90 are equal then sin^2 A/2, sin^2 B/2, sin^2 C/2 are in

If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P, prove that a, b, c are in A.P.

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

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

If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,c are in A.P.

If 1/a+1/(a-b)+1/c+1/(c-b)= 0 and a + c-b!=0 , then prove that a, b, c are in H.P.

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct