Question

In the class, the teacher is explaining how to solve a quadratic equation by completing the square method. He says that every quadratic equationa$x^2$+b$x$+c=0 can be written as $(Ax+B{)}^2$=C. Is he saying true or false?

• A. True
• B. False

Answer 1

The correct option is A

True

a$x^2$+b$x$+c=0 can be written as $x^2$+($\frac{b}{a}$)$x$+($\frac{c}{a}$)=0 [when we divide the entire equation with "a"]

This can be written as

$\Rightarrow$ $x^2$+($\frac{b}{a}$)$x$+($\frac{c}{a}$)=0

$\Rightarrow$$(x+\frac{b}{2a}{)}^2$-$(\frac{b}{2a}{)}^2$+$\frac{c}{a}$=0

i.e, it can be simplified as $(x+\frac{b}{2a}{)}^2$-($\frac{b^2-4ac}{4a^2}$)=0

Therefore $(x+\frac{b}{2a}{)}^2$ = ($\frac{b^2-4ac}{4a^2}$)

Every quadratic equation can be written as $(Ax+B{)}^2$=C

So, the teachers statement is true.