SOLUTION: when the sum of 4 and three times a positive number is subtracted from the square of the number, 0 results. Find the number

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Question 745833: when the sum of 4 and three times a positive number is subtracted from the square of the number, 0 results. Find the number
Answer by savvyhush23(50) About Me  (Show Source):
You can put this solution on YOUR website!
when the sum of 4 and three times a positive number is subtracted from the square of the number, 0 results. Find the number
let x is the number:
when the sum of 4 and three times a positive number: %284%2B3x%29
is subtracted from the square of the number, 0 results: x%5E2-%284%2B3x%29=0
x%5E2-3x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-4+=+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=%28-3%29%5E2-4%2A1%2A-4=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-3%29-sqrt%28+25+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-3x%2B-4 can be factored:
1x%5E2%2B-3x%2B-4+=+1%28x-4%29%2A%28x--1%29
Again, the answer is: 4, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-4+%29


Therefore the positive number is: 4