Pls answer the question with correct explaination
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Step-by-step explanation:We know that when roots of
quadratic equations are equal
then
) Discriminant (D) O
Given equation is ,
) (b-c)x2 (c-a)x +(a-b) 0
D (c-a)^2 - 4(b-c)(a-b) 0
(c^2 + a^2 -2ac) 4(ab -b 2 -
ac bc ) 0
=) c^2 + a^2 -2ac 4ab + 4b 2
+4ac -4bc O
a^2 + 4b^2 +c^2-4ab-4bc +
2ac 0
=) ( a -2b + c)^2 = 0
) a -2b + c = 0
=) a +c 2b --- --(1)
we can write this expression
as
) (b - a )= (c -b )
so this is required condition for
a, b,c therefore a, b,c are in
A.P
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