Question

8. If the roots of the equation (a-b)x 2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c.

Answer 1

Step-by-step explanation:

We know that,

If the quadratic equation=ax²+bx+c=0 whose roots are equal then it's deteminant is equal to zero.

=>(a-b)x²+(b-c)x+(c-a)=0

Deteminant =0

=>(b-c)² -4(a-b)(c-a)=0

=>b²+c²-2bc-4ac+4a²+4bc-4ab=0

=>b²+c²+4a²+4bc-4ac-4ab=0

=>b²+c²(-2a)²+2bc+2c(-2a)+2(-2a)b=0

=>(b+c-2a)²=0

=>b+c-2a=0

Therefore,

b+c=2a

Hence proved.

Mark me as a brainlist thankyou...