Posted by **Donni** on Monday, November 15, 2010 at 7:07pm.

i have very little information in my math book on the following questions. can you either tell me the answer or a link where i can find my own answer. thanks

How do you know if a quadratic equation will have one, two, or no solutions?

How do you find a quadratic equation if you are only given the solution?

- algebra -
**Henry**, Thursday, November 18, 2010 at 5:34pm
1. b^2 < 4ac: 2 imaginary solutions.

b^2 = 4ac: 1 real solution.

b^2 > 4ac: 2 real soutions.

2. Let's take a given Eq and solution

sets and use the solutions to derive the Eq.

Eq: y = 2x^2 + 5x + 2.

Solution set: x = -1/2, and x = -2.

x = -1/2,

x + 1/2 = 0.

x = -2,

x + 2 = 0.

(x + 1/2) (x + 2) = 0,

Multiply the 2 binomials:

x^2 + 2x + x/2 + 1 = 0,

x^2 + 5x/2 + 1 = 0,

Multiply both sides by 2 to eliminate the fraction and get:

2x^2 + 5x + 2 = 0.

The derived Eq is equivalent to the

given Eq.

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