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Question

In the class, the teacher is explaining how to solve a quadratic equation by completing the square method. He says that every quadratic equationax2+bx+c=0 can be written as (Ax+B)2 = C. Is it true or false?


  1. True

  2. False


Solution

The correct option is A

True


 ax2+bx+c=0 can be written as x2+(ba)x+(ca)=0 [when we divide the entire equation with "a"]

This can be written as

x2+(ba)x+(ca)=0

(x+b2a)2-(b2a)2+ca=0

i.e, it can be simplified as (x+b2a)2-(b24ac4a2)=0

Therefore (x+b2a)2 = (b24ac4a2)

Every quadratic equation can be written as (Ax+B)2 = C

So, the teachers statement is true.

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