Pa answer po please
Home
/
Pa answer po please
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
The Derivation of the Quadratic Formula
Step-by-step explanation:
The standard form of a quadratic equation is
where a, b, and c are real numbers.
First, we isolate the constant term c.
Reason: This is the first step in completing the square, and we must transform ax² + bx into a perfect square trinomial.
We then have this:
For the next step, we must divide the whole equation by a.
Reason: In order to perform completing the square, the coefficient of the quadratic term must be 1.
Then, we have this:
For the next step, we must follow the method of completing the square. Since we have the expression x² + (b/a)x, in order for it to become a perfect square trinomial, we must add to both sides the square of half of b.
Reason: We must make x² + (b/a)x a perfect square trinomial by means of completing the square.
These are the following lines in the derivation:
From here, we can now factor the left side of the equation as a perfect square trinomial.
Reason: By factoring, the value of x will easily be deduced.
Now, we have this:
Here, we can extract the square roots of both sides.
Reason: We extract the square roots in order to remove the exponent 2 above x + b/2a.
By extracting the square roots, we should have this:
Since a, b, and c are real numbers, the square root of a constant has a positive and negative counterparts (I can't add the ± symbol).
In order to isolate x, we transpose b/2a to the right side of the equation.
Reason: We must isolate x in order to create a formula which produces two solutions for any given values of a, b, and c.
By doing so, we have:
Since the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator, we can reduce 4a² to 2a.
Now, we can combine the fractions since they have common denominators:
And we have successfully derived the quadratic formula.