SOLUTION: These are difficult to figure out. Can someone please explains these to me? 1.) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equa

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: These are difficult to figure out. Can someone please explains these to me? 1.) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equa      Log On


   

Question 606058: These are difficult to figure out. Can someone please explains these to me?
1.) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0
The solutions are -10, 1
The equation is ____ = 0
2.) Solve:
x^2 - x + 10 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1.) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0
The solutions are -10, 1
---------
(x - (-10))*(x - 1) = 0
x%5E2+%2B+9x+-+10+=+0
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2.) Solve:
x^2 - x + 10 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B10+=+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=%28-1%29%5E2-4%2A1%2A10=-39.

The discriminant -39 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -39 is + or - sqrt%28+39%29+=+6.2449979983984.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B10+%29