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My name is Ann [436]
2 years ago
10

When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to crea

te a perfect square trinomial?
Mathematics
2 answers:
____ [38]2 years ago
7 0

Answer:

According to steps 2 and 4. The second-order polynomial must be added by -c and b^{2} to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form a\cdot x^{2} + b\cdot x + c = 0, \forall \,x \in\mathbb{R}. The procedure is presented below:

1) a\cdot x^{2} + b\cdot x + c = 0 (Given)

2) a\cdot x^{2} + b \cdot x = -c (Compatibility with addition/Existence of additive inverse/Modulative property)

3) 4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c (Compatibility with multiplication)

4) 4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c (Compatibility with addition/Existence of additive inverse/Modulative property)

5) (2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by -c and b^{2} to create a perfect square trinomial.

atroni [7]2 years ago
3 0

it can also be explained as D on edg if you still needed the answer :)

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