Question and answer
Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions? Explain why.
Answer: There are couple of different ways you could look at this. The solution to ax^2 + bx + c = 0 is basically the quadratic formula, [ x = [ -b ± v(b^2 - 4ac) ] / 2a This means you really only have two solutions: x = [ -b + v(b^2 - 4ac) ] / 2a x = [ -b - v(b^2 - 4ac) ] / 2a What really helps determine the type and number of solutions is the discriminant: b^2 - 4ac. If this is less than
0, then you'll have the square root of a negative number in both solutions, giving you two complex solutions. Notice that you can't have one real solution and one complex solution, because if you have the square root of a negative number in one solution, then you must have it in the second solution too. If b^2 - 4ac > 0, then you'll have two different, real solutions, because you'll get a different number for each solution. And finally, if b^2 - 4ac = 0, then the two solutions will both be -b / 2a, which means you really only have one unique real solution. Another way to think about this is to look at the graph. The graph of y = ax^2 + bx + c is a parabola. When y=0, that means the parabola is crossing the x-axis. It could cross it in two points, or one point (where the vertex is just touching the axis), or no points (e.g. if the vertex is above the x-axis and the parabola is opening upward). In this last case, the two solutions would be complex, not real. ]
Expert answered|marissa-sarol|Points 81|
Question
Asked 6/18/2013 9:35:33 PM
0 Answers/Comments
Get an answer
New answers
Rating

There are no new answers.

Comments

There are no comments.

Add an answer or comment
Log in or sign up first.
21,047,880 questions answered
Popular Conversations
__________ is someone whose opinion is valued in the decision-making ...
Weegy: The INFLUENCER is someone whose opinion is valued in the decision-making process. User: the person who ...
5/23/2015 12:34:09 PM| 2 Answers
What does polynomial mean?
Weegy: The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in its canonical ...
5/23/2015 12:53:01 PM| 2 Answers
simplify each expression use positive exponents m^3n^-6p^0 User: ...
Weegy: The explicit formula that represents the geometric sequence -2, 8, -32, 128 is an = -2*(-4)^(n - 1) . common ...
5/23/2015 9:28:41 PM| 2 Answers
It is expected that US forests will _______. a. not be able to meet ...
Weegy: It is expected that US forests will provide increasingly cheaper timber. User: Which of the following best ...
5/23/2015 11:00:26 PM| 2 Answers
Weegy Stuff
S
L
Points 706 [Total 1236]| Ratings 2| Comments 686| Invitations 0|Offline
S
Points 515 [Total 523]| Ratings 1| Comments 505| Invitations 0|Offline
S
1
Points 460 [Total 852]| Ratings 1| Comments 450| Invitations 0|Offline
S
P
C
L
P
L
1
P
P
1
P
1
Points 248 [Total 8994]| Ratings 0| Comments 248| Invitations 0|Offline
S
L
P
Points 248 [Total 2725]| Ratings 0| Comments 248| Invitations 0|Offline
S
1
L
L
Points 67 [Total 8250]| Ratings 0| Comments 67| Invitations 0|Offline
S
L
Points 56 [Total 3810]| Ratings 2| Comments 36| Invitations 0|Offline
S
Points 33 [Total 53]| Ratings 0| Comments 33| Invitations 0|Offline
S
L
1
R
Points 28 [Total 1315]| Ratings 0| Comments 28| Invitations 0|Offline
S
Points 14 [Total 14]| Ratings 0| Comments 14| Invitations 0|Offline
Home | Contact | Blog | About | Terms | Privacy | Social | ©2015 Purple Inc.