Question

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

Answer 1

Answer:

roots of a quadratic equation are equal, then the discriminant of the quadratic equation is 0.

D=b2−4ac=0D=b2−4ac=0

(b−c)x2+(c−a)x+(a−b)=0 ≡ ax2+bx+c=0(b−c)x2+(c−a)x+(a−b)=0 ≡ ax2+bx+c=0

Here, a =(b-c) , b = (c-a) and c = (a-b)

So, D = (c−a)2−4(b−c)(a−b)=0(c−a)2−4(b−c)(a−b)=0

c2+a2−2ac−4(ab−b2−ac+bc)=0c2+a2−2ac−4(ab−b2−ac+bc)=0

c2+a2−2ac−4ab+4b2+4ac−4bc=0c2+a2−2ac−4ab+4b2+4ac−4bc=0

c2+a2+2ac+4b2−4ab−4bc=0c2+a2+2ac+4b2−4ab−4bc=0

(c+a)2+4b2−4b(a+c)=0(c+a)2+4b2−4b(a+c)=0

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