Intermediate Single-Variable Algebra - Math
Card 0 of 448
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
Compare your answer with the correct one above
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
Compare your answer with the correct one above
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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Consider the equation 
.
According to the Rational Zeroes Theorem, if 
are all integers, then, regardless of their values, which of the following cannot be a solution to the equation?
Consider the equation
According to the Rational Zeroes Theorem, if
By the Rational Zeroes Theorem, any rational solution must be a factor of the constant, 6, divided by the factor of the leading coefficient, 14.
Four of the answer choices have this characteristic:
is in lowest terms, and 3 is not a factor of 14. It is therefore the correct answer.
By the Rational Zeroes Theorem, any rational solution must be a factor of the constant, 6, divided by the factor of the leading coefficient, 14.
Four of the answer choices have this characteristic:
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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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