Quadratic Equations and Inequalities - Math
Card 0 of 264
Given 
, what is the value of the discriminant?
Given
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:
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:
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:
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
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:
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:
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:
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 quadratic equation using any method:
Solve the quadratic equation using any method:
Use the quadratic formula to solve:
Use the quadratic formula to solve:
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Find the zeros.
Find the zeros.
Factor the equation to 
. Set both equal to zero and you get 
and 
. Remember, the zeros of an equation are wherever the function crosses the 
-axis.
Factor the equation to
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Find the zeros.
Find the zeros.
Factor out an 
from the equation so that you have  "x(x-10)")
. Set 
and 
equal to 
. Your roots are 
and 
.
Factor out an
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Find the zeros.
Find the zeros.
Set 
equal to zero and you get 
. Set 
equal to zero as well and you get 
and 
because when you take a square root, your answer will be positive and negative.
Set
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Find the zeros.
Find the zeros.
Factor out a 
from the entire equation. After that, you get 
. Factor the expression to 
. Set both of those equal to zero and your answers are 
and 
.
Factor out a
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Find the zeros.
Find the zeros.
This expression is the difference of perfect squares. Therefore, it factors to
. Set both of those equal to zero and your answers are 
and 
.
This expression is the difference of perfect squares. Therefore, it factors to
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Find the zeros.
Find the zeros.
Factor the equation to 
. Set both equal to 
and you get 
and 
.
Factor the equation to
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Find the zeros.
Find the zeros.
Factor a 
out of the quation to get
which can be further factored to
.
Set the last two expressions equal to zero and you get 
and 
.
Factor a
which can be further factored to
Set the last two expressions equal to zero and you get
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Find the zeros.
Find the zeros.
Set each expression equal to zero and you get 0 and 6.
Set each expression equal to zero and you get 0 and 6.
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Find the zeros.
Find the zeros.
Set both expressions equal to 
. The first factor yields 
. The second factor gives you 
.
Set both expressions equal to
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Find the zeros.
Find the zeros.
Set both expressions to 
and you get 
and 
.
Set both expressions to
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Solve the following equation by factoring.
Solve the following equation by factoring.
We can factor by determining the terms that will multiply to –8 and add to +7.
Our factors are +8 and –1.
Now we can set each factor equal to zero and solve for the root.
We can factor by determining the terms that will multiply to –8 and add to +7.
Our factors are +8 and –1.
Now we can set each factor equal to zero and solve for the root.
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