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.
19,248,158 questions answered
Popular Conversations
The square of a certain negative number is equal to five more than ...
Weegy: x^2 = 0.5x + 5 Quadratic formula gives solutions as: -2 and 2.5, but since x is negative, it's -2. User: ...
1/29/2015 9:17:38 AM| 4 Answers
7x + 2y = 4 y = x + 1 Solve the system of equations. no ...
Weegy: The best answer is B.11y = -55 User: The y-intercept of the line whose equation is 3x - 2y = 6 is -3 2 6 ...
1/29/2015 10:12:58 AM| 4 Answers
What is the resulting equation when the expression for y in the ...
Weegy: 3x + y = 1 3x + (6 - 4x) =1 3x + 6 - 4x =1 ............3x - 4x + 6 = 1.......-x + 6 = 1 The first choice... ...
1/29/2015 12:32:25 PM| 4 Answers
In your notebook, set up the following subtraction in a vertical ...
Weegy: Answer = 12 = (2.5/-5) x -6 = -2 x -6 =12 User: Identify the polynomial. a 2 + bcd 3 ...
1/29/2015 8:54:54 PM| 4 Answers
The slope of the line passing through the points (-1, 5) and (3, 5) ...
Weegy: (-1) * 5 = -5 User: what is the slope of the line passing thru (0,4) and (-8,-1) User: What is the slope of ...
1/29/2015 4:21:11 AM| 2 Answers
true or false. A pronoun is a noun substitute.
Weegy: They is a pronoun. User: true or false. A noun indicates the action in a sentence.
1/29/2015 8:22:51 AM| 2 Answers
Weegy Stuff
S
L
Points 2094 [Total 2115]| Ratings 0| Comments 2094| Invitations 0|Offline
S
L
P
L
P
Points 1428 [Total 6705]| Ratings 0| Comments 1428| Invitations 0|Offline
S
1
L
1
L
P
P
L
P
P
Points 716 [Total 15727]| Ratings 1| Comments 706| Invitations 0|Offline
S
L
Points 438 [Total 1119]| Ratings 2| Comments 418| Invitations 0|Offline
S
1
L
L
Points 310 [Total 7010]| Ratings 1| Comments 300| Invitations 0|Offline
S
Points 121 [Total 136]| Ratings 1| Comments 111| Invitations 0|Offline
S
P
C
L
P
L
1
Points 92 [Total 6680]| Ratings 1| Comments 82| Invitations 0|Offline
S
L
Points 83 [Total 1644]| Ratings 0| Comments 83| Invitations 0|Online
S
Points 63 [Total 445]| Ratings 0| Comments 63| Invitations 0|Offline
S
Points 50 [Total 52]| Ratings 0| Comments 0| Invitations 5|Offline
Home | Contact | Blog | About | Terms | Privacy | Social | ©2014 Purple Inc.