SOLUTION: What three techniques can be used to solve a quadratic equation, demonstrate each using x^2-10x-39=0

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Question 203639: What three techniques can be used to solve a quadratic equation, demonstrate each using x^2-10x-39=0
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
To solve:
x^2-10x-39=0
.
Three techniques could be:
1. factoring
2. completing the square
3. quadratic equation
.
Three techniques could be:
1. factoring
x^2-10x-39=0
(x-13)(x+3)=0
x = {-3, 13}
.
2. completing the square
x^2-10x-39=0
x^2-10x = 39
x^2-10x+25 = 39+25
(x-5)^2 = 64
(x-5) = sqrt(64)
x-5 = +-(8)
x = +-(8)+5
x = {-3, 13}
.
3. quadratic equation
x^2-10x-39=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=256 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 13, -3. Here's your graph:
.
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