SOLUTION: Given X^2+XY+AY^2=B and A=1, B=7, find the x intercepts.

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Question 111621: Given X^2+XY+AY^2=B and A=1, B=7, find the x intercepts.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
x%5E2%2Bxy%2Bay%5E2=b+
a=1, b=7,
find the x_+intercepts.


x%5E2+%2B+xy+%2B+ay%5E2+=+b+ ………plug in a=1, b=7,

x%5E2+%2B+y%28x+%2B+y%29+=+7+……..to find x_+intercepts put y=0
So, you will have
x%5E2+%2B+x%2A0+%2B1%2A0%5E2+=+7+……..
x%5E2+=+7+……..
x+=+sqrt%287+%29……..
x+=+%282.65%29
x_+intercepts are 2.65%2C+0 and -2.65%2C+0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-7+=+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=%280%29%5E2-4%2A1%2A-7=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+2.64575131106459
x%5B2%5D+=+%28-%280%29-sqrt%28+28+%29%29%2F2%5C1+=+-2.64575131106459

Quadratic expression 1x%5E2%2B0x%2B-7 can be factored:
1x%5E2%2B0x%2B-7+=+%28x-2.64575131106459%29%2A%28x--2.64575131106459%29
Again, the answer is: 2.64575131106459, -2.64575131106459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-7+%29