SOLUTION: Yet more issues, will this homework never end? 1. Find the x-intercepts y = x² + 4x – 1 2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many r

Algebra ->  College  -> Linear Algebra -> SOLUTION: Yet more issues, will this homework never end? 1. Find the x-intercepts y = x² + 4x – 1 2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many r      Log On


   

Question 185908: Yet more issues, will this homework never end?
1. Find the x-intercepts
y = x² + 4x – 1

2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many real number solutions exist for the equation.
y = x² + 8x + 16
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Yet more issues, will this homework never end?
It will end once you're out of school and in prison.
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1. Find the x-intercepts
The x-intercepts are where the graph crosses the x-axis and y = 0. These are the zeroes of the equation, the values of x that make the eqn = 0. In other words, the answers.
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y = x² + 4x – 1
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-1=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+0.23606797749979
x%5B2%5D+=+%28-%284%29-sqrt%28+20+%29%29%2F2%5C1+=+-4.23606797749979

Quadratic expression 1x%5E2%2B4x%2B-1 can be factored:
1x%5E2%2B4x%2B-1+=+%28x-0.23606797749979%29%2A%28x--4.23606797749979%29
Again, the answer is: 0.23606797749979, -4.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-1+%29

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2. Evaluate the discriminant b² - 4ac. Then use the answer to state how many real number solutions exist for the equation.
y = x² + 8x + 16
The onsite solver does a good job of that.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B-16+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A-16=128.

Discriminant d=128 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+128+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+128+%29%29%2F2%5C1+=+1.65685424949238
x%5B2%5D+=+%28-%288%29-sqrt%28+128+%29%29%2F2%5C1+=+-9.65685424949238

Quadratic expression 1x%5E2%2B8x%2B-16 can be factored:
1x%5E2%2B8x%2B-16+=+%28x-1.65685424949238%29%2A%28x--9.65685424949238%29
Again, the answer is: 1.65685424949238, -9.65685424949238. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-16+%29