SOLUTION: Which statement must be true if a parabola represented by the equation y = ax^2 + bx + c does not intersect the x-axis? b^2 � 4ac = 0 b^2 � 4ac

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Question 253299: Which statement must be true if a parabola represented by the equation y = ax^2 + bx + c does not intersect the x-axis?
b^2 � 4ac = 0
b^2 � 4ac < 0
b^2 � 4ac > 0, and b^2 � 4ac is a perfect square.
b^2 � 4ac > 0, and b^2 � 4ac is not a perfect square
Found 3 solutions by drk, Alan3354, JimboP1977:
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website!
The answer is:
b2 � 4ac < 0
This will give you a negative discriminant which means imaginary or no solutions.

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
b2 � 4ac < 0
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This is covered well by the on-site solver:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -16 is + or - .

The solution is , or
Here's your graph:

Answer by JimboP1977(311)   (Show Source):
You can put this solution on YOUR website!
b^2-4ac <0

SOLUTION: Which statement must be true if a parabola represented by the equation y = ax^2 + bx + c does not intersect the x-axis? b^2 � 4ac = 0 b^2 � 4ac < 0 b^2 � 4ac > 0, and b^2 �