The roots of the equation (b-c)x^2 + (c-a)x + (a-b) =0 are
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♥️HEY MATE♥️
.HERE IS THE ANSWER TO YOUR QUESTION....
If the roots of the equation (b-c) x^2+(c-a) x+(a-b) =0 are equal, then how can I prove that 2b=a+c?
(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
I HOPE IT HELPED YOU.IF IT DID THEN PLEASE MARK AS BRIANLIEST AND FOLLOW ME♥️♥️
.HERE IS THE ANSWER TO YOUR QUESTION....
If the roots of the equation (b-c) x^2+(c-a) x+(a-b) =0 are equal, then how can I prove that 2b=a+c?
(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
I HOPE IT HELPED YOU.IF IT DID THEN PLEASE MARK AS BRIANLIEST AND FOLLOW ME♥️♥️
akshitask153:
Tysm for answering but in the question I don't have any prooving part...it's only to find roots
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