Understanding Quadratic Equations - Math
Card 1 of 92
Given 
, what is the value of the discriminant?
Given
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In general, the discriminant is 
.
In this particual case 
.
Plug in these three values and simplify: 
In general, the discriminant is
In this particual case
Plug in these three values and simplify:
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are 
imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are irrational roots.
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Given , what is the value of the discriminant?
Given
Tap to reveal answer
In general, the discriminant is .
In this particual case .
Plug in these three values and simplify:
In general, the discriminant is
In this particual case
Plug in these three values and simplify:
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
Tap to reveal answer
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are irrational roots.
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Given , what is the value of the discriminant?
Given
Tap to reveal answer
In general, the discriminant is .
In this particual case .
Plug in these three values and simplify:
In general, the discriminant is
In this particual case
Plug in these three values and simplify:
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
Tap to reveal answer
The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
Tap to reveal answer
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are irrational roots.
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Solve the following equation using the quadratic form:
Solve the following equation using the quadratic form:
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Factor the equation and solve:
or
Therefore there are four answers:
Factor the equation and solve:
or
Therefore there are four answers:
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Solve the following equation using the quadratic form:
Solve the following equation using the quadratic form:
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Factor the equation and solve:
or
This has no solutions.
Therefore there is only one answer:
Factor the equation and solve:
or
This has no solutions.
Therefore there is only one answer:
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Given , what is the value of the discriminant?
Given
Tap to reveal answer
In general, the discriminant is .
In this particual case .
Plug in these three values and simplify:
In general, the discriminant is
In this particual case
Plug in these three values and simplify:
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
Tap to reveal answer
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are irrational roots.
The formula for the discriminant is:
Since the discriminant is positive and not a perfect square, there are
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Use the discriminant to determine the nature of the roots:
Use the discriminant to determine the nature of the roots:
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The formula for the discriminant is:
Since the discriminant is negative, there are imaginary roots.
The formula for the discriminant is:
Since the discriminant is negative, there are
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Solve the equation for 
.
Solve the equation for
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Cross multiply.
Set the equation equal to zero.
Factor to find the roots of the polynomial.
and 
Cross multiply.
Set the equation equal to zero.
Factor to find the roots of the polynomial.
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Evaluate 
Evaluate
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In order to evaluate 
one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.
Multiply terms by way of FOIL method.
Now multiply and simplify.
In order to evaluate
Multiply terms by way of FOIL method.
Now multiply and simplify.
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