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What three techniques can be used to solve a quadratic equation? Demonstrate all three techniques using the equation "3^2 + x - 2 = 0.

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David Shabazi Profile
David Shabazi answered

The three techniques are factoring, factor by grouping, and completing the square.

Factoring:

  • Step 1) Create a factor chart for all factor pairs of c
    • A factor pair is just two numbers that multiply and give you 'C'
  • Step 2) Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b
  • Step 3) Insert the pair you found in step 2 into twobinomals
  • Step 4) Solve each binomial for zero to get the solutions of the quadratic equation.
Factor by grouping:

  • Step 1) Determine the product of AC (the coefficientsin the quadratic equation Ax^2 + Bx + C = 0)
  • Step 2) Determine what factors of a⋅c sums up to b.
  • Step 3) "ungroup" the middle term to become the sum of the factors found in step 2
  • Step 4) group the pairs.
Completing the square:

The process for finding the last term of a perfect square trinomial.

However, in this case, 3x^2 + x - 2 = 0 is not a perfect square trinomial, so we cannot use "Completing the square" as a method of solving the quadratic equation.

I'm going to be honest: Using the quadratic equation to solve these equations is much, MUCH easier than these three other methods. It may seem more time consuming, but it's a method that you KNOW will work for sure. So let's go ahead and do that:

x = {-1 ± √(1)^2 - 4(3)(-2)}/2(3)

= (-1 ± √25)/6

= (-1 ± 5)/6

Your two answers will be: (-1 + 5)/6 and (-1 - 5)/6, which simplifies to 2/3 and -1.

thanked the writer.
John McCann
John McCann commented
, 3x^2 + x - 2 = 0


On college algebra you will do these ugly quadratics by completing the square.

Some very ugly fractions result.

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