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Dennis_Churaev [7]
2 years ago
15

The steps to derive the quadratic formula are shown below:

Mathematics
2 answers:
prohojiy [21]2 years ago
7 0

Answer:

\huge\boxed{\sf Option \ B}

Step-by-step explanation:

<h3>Step 3:</h3>

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

<h3>The next step will be:</h3>
  • to find the b² for the expression on the left.
<h3>How to find b²:</h3>

Take the expression

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

<u>We can also write it as:</u>

\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}

kvv77 [185]2 years ago
5 0

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

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