Question

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

ANSWER:–

Hi,

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.

I hope this helps you.

please mark as brilliant answer ✌✌

thanks

Answer 2

plz refer to this attachment