SOLUTION: the directions of my homework say , "state the value of the discrimnant for each equation. Then determine the number of real roots of the equation." I'm not sure how to solve the p

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the directions of my homework say , "state the value of the discrimnant for each equation. Then determine the number of real roots of the equation." I'm not sure how to solve the p      Log On


   

Question 298071: the directions of my homework say , "state the value of the discrimnant for each equation. Then determine the number of real roots of the equation." I'm not sure how to solve the problems. For example one of the problems are "q^2+4q+3=0"
thanks!!!
Found 2 solutions by rapaljer, jim_thompson5910:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is the quantity inside the radical of the quadratic formula. This is b%5E2+-+4ac. It turns out that if the discriminant is positive, then there will be two real roots; if the discriminant is 0, then there will be one (double!) real root; and if the discriminant is negative, there will be NO real roots--in other words the roots will be complex.

In your example, x%5E2+%2B4x%2B3=0, the discriminant is 4%5E2+-4%2A1%2A3, which is 16-12=4. Since this is positive, there are TWO real roots.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

From q%5E2%2B4q%2B3 we can see that a=1, b=4, and c=3


D=b%5E2-4ac Start with the discriminant formula.


D=%284%29%5E2-4%281%29%283%29 Plug in a=1, b=4, and c=3


D=16-4%281%29%283%29 Square 4 to get 16


D=16-12 Multiply 4%281%29%283%29 to get %284%29%283%29=12


D=4 Subtract 12 from 16 to get 4


Since the discriminant is greater than zero, this means that there are two real solutions.