Simple Maths: Solving Quadratic Equation Using Quadratic Formula

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Simple Maths: Solving Quadratic Equation Using Quadratic Formula

quadratic formula Maths Mathematics

Well, Most times, the most simple method of solving ax^2 + bx + c = 0 for the value of x is to factorize the quadratic, that is by setting each of the factors equal to zero and then solving each of the factors. But at times the equation may seem too messy, or probably doesn’t factorize at all, or you are not just in a mood to factorize. This is where the almighty quadratic formula sets in.

Also, while factorization might not always be successful, the Almighty Quadratic Formula will always find a solution.

Solving Quadratic Equations will the Almighty Quadratic Formula makes use of the “a”, “b”, and “c” from the general expression ax^2 + bx + c, where “a”, “b”, and “c” are the numerical coefficients of the quadratic expression or equation.

The Almighty Quadratic Formula is actually derived from solving the general quadratic expression using the process of completing the square, and is formally stated as x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

Derive quadratic formula

Meanwhile, for the Quadratic Formula to work, your equation must be arranged in the form of quadratic expression and equated to Zero. Also, note that the “2a” in the denominator of the Almighty Formula is underneath everything above, not just the square root. Make sure that you are careful never to drop the square root or the “plus/minus” in the middle of your calculations in order not to forget to put them back. Remember that b^2 means “the square of ALL of b, not neglecting its sign”, but don’t leave b^2 being negative, because even if b is negative, the square of a negative is a positive.

For Example :

Solve x^2 + 3x – 4 = 0
Though this quadratic equation happens to be factorizable:

x^2 + 3x – 4 = (x + 4)(x – 1) = 0

…therfore I already know that the solutions are x = –4 and x = 1.
Then using the Almighty Quadratic Formula, where a = 1, b = 3, and c = –4, my solution looks like this:

Quadratic equation formula image

Then, as expected, the answers are x = –4, x = 1.

Another Example :

2x^2 – 4x – 3 = 0.

In this case, since there are no factors of (2)(–3) = –6 that add up to –4, so this equation cannot be factorized. We apply the Quadratic Formula. In this case, a = 2, b = –4, and c = –3:

Quadratic equation

Then our answers ares x = –0.58, x = 2.58, both rounded to two decimal places.

Last Example :
x^2 + 4x + 5 = 0

That should be all on Solving Quadratic Equation Using Quadatic Formula.

DOWNLOAD PDF : Quadratic Equation With Formula

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