Question

if the roots of the equation (b-c)x2+(c-a)x+(a-b)=0 and are equal ,prove that 2b=a+c​

Answer 1

Answer:

Step-by-step explanation:

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

Answer goes like this .....................

(b-c)x²+(c-a)x+(a-b)=0

compare the 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

Answer 2

plz refer to this attachment