Intermediate Single-Variable Algebra - Math
Card 1 of 448
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:
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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:
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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
Tap to reveal 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:
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:
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
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
← Didn't Know|Knew It →
Solve the quadratic equation using any method:
Solve the quadratic equation using any method:
Tap to reveal answer
Use the quadratic formula to solve:
Use the quadratic formula to solve:
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
Factor out an 
from the equation so that you have  "x(x-10)")
. Set 
and 
equal to 
. Your roots are 
and 
.
Factor out an
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
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
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
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
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
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
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
Factor the equation to 
. Set both equal to 
and you get 
and 
.
Factor the equation to
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
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
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
Set each expression equal to zero and you get 0 and 6.
Set each expression equal to zero and you get 0 and 6.
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
Set both expressions equal to 
. The first factor yields 
. The second factor gives you 
.
Set both expressions equal to
← Didn't Know|Knew It →
Find the zeros.
Find the zeros.
Tap to reveal answer
Set both expressions to 
and you get 
and 
.
Set both expressions to
← Didn't Know|Knew It →