Math help Please!! ASAP

Question

Tyler was asked to solve the following quadratic equation using one of the 3 methods below:

x2+3x+2=0

Quadratic Formula, Factoring, Completing the Square

Which method should Tyler use that is more convenient? Explain

Answer 1

"Completing the Square" is unnecessary because the equation is already set to zero and the last coefficient can be factored easily. The Quadratic Formula would work, but it would take more than a few steps to do it. This means factoring is the most convenient method, so let's look a little closer at factoring. Factoring simply means that we unravel all the numbers that make up another number - it is breaking numbers down into their component numbers. In this particular case, the other number is represented by a quadratic equation, so students must become familiar with the FOIL method in order factor such equations. It will take plenty of practice factoring simpler quadratic equations, but you will eventually become more skilled and fluid about it, and you will begin to see the patterns in these equations. Try looking for a specific pattern of "numbers added and multiplied."

In the FOIL method, we multiply the "First" coefficients of each factor, then we multiply the "Outside" coefficients by one another, then we multiply the "Inside" coefficients by one another, and we "Add" the products of the "Outside" and "Inside" coefficients, and, finally, we multiply the "Last" coefficients of each factor. This gives us the First, Outside+Inside, and Last coefficients of the resulting quadratic equation. Now, turn this around, and break the quadratic equation into its two factors. We know that the "Last" number in the equation comes from multiplying the "Last" numbers of the two factors. We also know that the middle number (coefficient) comes from adding the same two numbers (the "Last" coefficients). So, you are seeking to recognize the two numbers that equal 3 when added, but they equal 2 when multiplied. That's why some people call this the "Add/Multiply" or "AM" method. Can you figure out quickly which two numbers equal 3 when added and equal 2 when multiplied?

Answer 2

Completing the square.

x^2 + 3x + 2 = 0

x^2 + 3x =. -2

Now compete the square on the left side by taking 1/2 of 3 and squaring that. (3/2)^2

x^2 + 3x + 9/4 = -2 + 9/4. Add the (3/2)^2 to both sides.

(x + 3/2)^2 = 1/4

Now take the root of both sides

x+ 3/2 = -1/4. and x + 3/2 = 1/4 Solve both of these equations.

Why does this work?

(x + a)^2 = (x + a)(x + a). =. x^2 + 2a + a^2. Notice that 3rd term is 1/2 of middle term then squared.

Answer 3

Factoring is a simple way.

Factor the left to get:

Find the roots of each term in the product seperately by settting each to zero and solving for x:

x + 1 = 0

x = -1

x + 2 = 0

x = -2

solution: x = -1 x = -2