SOLUTION: I need help. Please 1.Solve by applying the Quadratic Formula. Show your work. 2x2 + 7x + 3 = 0 2.Use the discriminant to determine whether the following equations have s

Algebra ->  Graphs -> SOLUTION: I need help. Please 1.Solve by applying the Quadratic Formula. Show your work. 2x2 + 7x + 3 = 0 2.Use the discriminant to determine whether the following equations have s      Log On


   

Question 246901: I need help. Please
1.Solve by applying the Quadratic Formula. Show your work.
2x2 + 7x + 3 = 0
2.Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
9 - 2a2 = 6a + 2
3.Solve by applying the Quadratic Formula. Show your work.
x2 + 4x - 7 = 0

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Do you know what the quadratic formula is?
Do you know what the discriminant is?
Look in the glossary (dictionary ) in your math book.
one problem per question please
This should help you
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B7x%2B3+=+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=%287%29%5E2-4%2A2%2A3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+-0.5
x%5B2%5D+=+%28-%287%29-sqrt%28+25+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B7x%2B3 can be factored:
2x%5E2%2B7x%2B3+=+2%28x--0.5%29%2A%28x--3%29
Again, the answer is: -0.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B7%2Ax%2B3+%29