SOLUTION: Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; ju

Algebra ->  Square-cubic-other-roots -> SOLUTION: Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; ju      Log On


   

Question 648818: Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions. Can someone help with these 3 questions please?
1. 2x2 + 5x + 5 = 0
2 3z2 + z - 1 = 0
3 m2 + m + 1 = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is the part of the quadratic formula that is inside the square root. That would be:
b%5E2+-+4ac



1. 2x%5E2+%2B+5x+%2B+5+=+0

In this case, b%5E2+-+4ac comes to:
25+-+4%282%29%285%29
25+-+80
-55........
No Real Solutions-it has two imaginary solutions (reason: negative discriminant
b%5E2+-4ac+%3C+0)

2 3z%5E2+%2B+z+-+1+=+0
In this case, b%5E2+-+4ac comes to:
1+-+4%283%29%28-1%29
1+%2B+12
13.......
Answer: Two Real Irrational Solutions (reason: 13 is positive, but not a perfect square)

3 m%5E2+%2B+m+%2B+1+=+0

In this case, b%5E2+-+4ac comes to:
1+-+4%281%29%281%29
1+-4
-3.......
No Real Solutions-it has two imaginary solutions (reason: negative discriminant
b%5E2+-+4ac%3C0)