Question

If the roots of the quadratic equation (a – b)x + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.

Answer 1

Explanation:

(a-b)x²+(b-c)x+(c-a)=0

Compare this with Ax²+Bx+C=0

we get,

A= (a-b),

B=(b-c),

C = (c-a),

Discreminant (D)=0

[ Since, roots are equal ]

=> B²- 4AC = 0

=> (b-c)²-4(a-b)(c-a) = 0

=> (b²+c²-2bc)-4(ac-a²-bc+ab)=0

=> b²+c²-2bc-4ac+4a²+4bc-4ab=0

=> b²+c²+2bc-4ac-4ab =0

=> (b+c)² -4a(c+b) = 0

=> (b+c)[ b+c -4a] = 0

=> b+c = 0 or

b+c -4a = 0

=> b+c = 4a

••••

Answer 2

Answer:

Step-by-step explanation: