Question

The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 Blank space, fill in the answer
Provide the next step to derive the quadratic formula.
Answer Choices: (see image)

Answer 1

Answer:

b)

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

Step-by-step explanation:

Step(i):-

Given quadratic equation ax² + bx + c = 0

step(ii):-

ax² + bx = -c

Step(iii):-

Dividing 'a' on both sides , we get

$\frac{ax^{2} +bx }{a} = \frac{-c}{a}$

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

Step(iv):-

Adding  $(\frac{b}{2 a} )^{2}$ on both sides , we get

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

Answer 2

Answer:

B

Step-by-step explanation: