Question

The steps to derive the quadratic formula are shown below:

Answer 1

Answer:

$\huge\boxed{\sf Option \ B}$

Step-by-step explanation:

Step 3:

$\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}$ --------------------(1)

The next step will be:

• to find the b² for the expression on the left.

How to find b²:

Take the expression

$\displaystyle x^2 + \frac{bx}{a}$

We can also write it as:

$\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )$

According to the formula $a^2+2ab+b^2$, the b of this expression is $\displaystyle \frac{b}{2a}$. So,

b² will be:

$\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}$

So, we will add $\displaystyle \frac{b^2}{4a^2}$ to both sides in Eq. (1)

For STEP 4, the equation will become:

$\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}$

$\rule[225]{225}{2}$

Answer 2

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared