(a-b) x²+(b-c) x+(c-a), it\'s roots are equal, then prove that 2a=b+c

1.	(a-b) x²+(b-c) x+(c-a), it\'s roots are equal, then prove that 2a=b+c
Answer» We know that,If the quadratic equation ax²+bx+c=0whose roots are equal then it\'s deteminant is equal to zero.(a-b)x²+(b-c)x+(c-a)=0Deteminant =0(b-c)² -4(a-b)(c-a)==0b²+c²-2bc-4ac+4a²+4bc-4ab=0b²+c²+4a²+4bc-4ac-4ab=0b²+c²+(-2a)²+2bc+2c(-2a)+2(-2a)b=0(b+c-2a)²=0b+c-2a=0Therefore,b+c=2aHence proved.I hope this helps you.

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