Question

Show that the roots of the quadratic equation:
(b - x + (- ax + (1 - 1) = 0
are equal if c + a = 2b.​

Answer 1

Answer:

Roots will be equal if and only if Discriminant is equal to 0 i.e b^2-4ac=0......so in above quadratic equation b can be replaced with (c-a)

and a =(b-c) and c=(a-b).so putting value of a,b,c in above equation we have.

(c-a)^2-4(b-c)*(a-b)

=> (c-a)^2=4(b-c)(a-b)

=> c^2+a^2-2ac=4(ab-b^2-ac+cb)

=> C^2+a^2-2аc=4ab-4b^2-4ac+4cb

=> c^2+a^2-2ac +4ac-4ab-4b^2+4cb

=> (c+a)^2+(2b)^2-4ab+cb)=0

=> (c+a)^2+(2b)^2-2(2b)(a+c)=0

=> (c+a-2b)^2 =0

= c+a = 2b