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If the roots of the equation (b - c) x square (c-a) x (a-b) =0 are equal, prove that 2b =a + c. Its urgent help me?
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If the roots of the equation (b - c) x square (c-a) x (a-b) =0 are equ...

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If the roots of the equation (b - c) x square (c-a) x (a-b) =0 are equ...
Given that the quadratic equation,
(b-c)x²+(c-a)x+(a-b)=0,
has two equal roots,
then discriminant=0,
b²-4ac=0,
(c-a)²-4(b-c)(a-b)=0,
c²+a²-2ac-(4(ab-b²-ca+bc))=0,
c²+a²-2ac-4ab+4b²+4ac-4bc=0,
c²+a²+2ac-4ab+4b²-4bc=0
on further simplification,
2b=a+c
Community Answer
If the roots of the equation (b - c) x square (c-a) x (a-b) =0 are equ...
Your answer is here...

(b-c)x²+(c-a)x+(a-b)=0

Comparing with quadratic equation

Ax²+Bx+C=0

A=(b-c),
B=c-a,
C=a-b

Discriminate when roots are equal

D=B²-4AC=0

D=(c-a)²−4(b-c)(a-b)=0

D=(c²+a²−2ac)-4(ba-ac-b²+bc)=0

D=c²+a²−2ac-4ab+4ac+4b²-4bc=0

c²+a²+2ac-4b(a+c)+4b²=0

(a+c)²-4b(a+c)+4b²=0

[(a+c)-2b]²=0

a+c=2b
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