Quadratic Roots - Algebra 2
Card 0 of 56
Solve for 
:
Solve for
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To solve this equation, you must first eliminate the exponent from the 
by taking the square root of both sides:
Since the square root of 36 could be either 
or 
, there must be 2 values of 
. So, solve for
and
to get solutions of 
.
To solve this equation, you must first eliminate the exponent from the
Since the square root of 36 could be either
and
to get solutions of
Write a quadratic equation in the form 
with 2 and -10 as its roots.
Write a quadratic equation in the form
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Write in the form 
where p and q are the roots.
Substitute in the roots:
Simplify:
Use FOIL and simplify to get
.
Write in the form
Substitute in the roots:
Simplify:
Use FOIL and simplify to get
Give the solution set of the equation 
.
Give the solution set of the equation
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Using the quadratic formula, with 
:
Using the quadratic formula, with
Give the solution set of the equation 
.
Give the solution set of the equation
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Using the quadratic formula, with 
:
Using the quadratic formula, with
Let
Determine the value of x.
Let
Determine the value of x.
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To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.
Now we need to separate our equation in two and solve for each x.
or 
To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.
Now we need to separate our equation in two and solve for each x.
Write a quadratic equation in the form 
that has 
and 
as its roots.
Write a quadratic equation in the form
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1. Write the equation in the form 
where 
and 
are the given roots.
2. Simplify using FOIL method.
1. Write the equation in the form
2. Simplify using FOIL method.
Give the solution set of the following equation:
Give the solution set of the following equation:
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Use the quadratic formula with 
, 
and 
:
Use the quadratic formula with
Give the solution set of the following equation:
Give the solution set of the following equation:
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Use the quadratic formula with 
, 
, and 
:
Use the quadratic formula with
Find the roots of the following quadratic polynomial:
Find the roots of the following quadratic polynomial:
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To find the roots of this equation, we need to find which values of 
make the polynomial equal zero; we do this by factoring. Factoring is a lot of "guess and check" work, but we can figure some things out. If our binomials are in the form 
, we know 
times 
will be 
and 
times 
will be 
. With that in mind, we can factor our polynomial to
To find the roots, we need to find the 
-values that make each of our binomials equal zero. For the first one it is 
, and for the second it is 
, so our roots are 
.
To find the roots of this equation, we need to find which values of
To find the roots, we need to find the
Find the roots of 
.
Find the roots of
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When we factor, we are looking for two number that multiply to the constant, 
, and add to the middle term, 
. Looking through the factors of 
, we can find those factors to be 
and 
.
Thus, we have the factors:
.
To solve for the solutions, set each of these factors equal to zero.
Thus, we get 
, or 
.
Our second solution is, 
, or 
.
When we factor, we are looking for two number that multiply to the constant,
Thus, we have the factors:
To solve for the solutions, set each of these factors equal to zero.
Thus, we get
Our second solution is,
Write a quadratic function in standard form with roots of -1 and 2.
Write a quadratic function in standard form with roots of -1 and 2.
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From the zeroes we know
Use FOIL method to obtain:
From the zeroes we know
Use FOIL method to obtain:
Select the quadratic equation that has these roots:
Select the quadratic equation that has these roots:
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FOIL the two factors to find the quadratic equation.
First terms:
Outer terms:
Inner terms:
Last terms:
Simplify:
FOIL the two factors to find the quadratic equation.
First terms:
Outer terms:
Inner terms:
Last terms:
Simplify:
Solve for a possible root: 
Solve for a possible root:
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Write the quadratic equation.
The equation 
is in the form 
.
Substitute the proper coefficients into the quadratic equation.
The negative square root can be replaced by the imaginary term 
. Simplify square root 60 by common factors of numbers with perfect squares.
Simplify the fraction.
A possible root is: 
Write the quadratic equation.
The equation
Substitute the proper coefficients into the quadratic equation.
The negative square root can be replaced by the imaginary term
Simplify the fraction.
A possible root is:
Solve for the roots (if any) of 
Solve for the roots (if any) of
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Pull out a common factor of negative four.
The term inside the parentheses can be factored.
Set the binomials equal to zero and solve for the roots. We can ignore the negative four coefficient.
The answers are: 
Pull out a common factor of negative four.
The term inside the parentheses can be factored.
Set the binomials equal to zero and solve for the roots. We can ignore the negative four coefficient.
The answers are:
Solve for :
Solve for
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To solve this equation, you must first eliminate the exponent from the by taking the square root of both sides:
Since the square root of 36 could be either or , there must be 2 values of . So, solve for
and
to get solutions of .
To solve this equation, you must first eliminate the exponent from the
Since the square root of 36 could be either
and
to get solutions of
Write a quadratic equation in the form with 2 and -10 as its roots.
Write a quadratic equation in the form
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Write in the form where p and q are the roots.
Substitute in the roots:
Simplify:
Use FOIL and simplify to get
.
Write in the form
Substitute in the roots:
Simplify:
Use FOIL and simplify to get
Give the solution set of the equation .
Give the solution set of the equation
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Using the quadratic formula, with :
Using the quadratic formula, with
Give the solution set of the equation .
Give the solution set of the equation
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Using the quadratic formula, with :
Using the quadratic formula, with
Let
Determine the value of x.
Let
Determine the value of x.
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To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.
Now we need to separate our equation in two and solve for each x.
or
To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.
Now we need to separate our equation in two and solve for each x.
Write a quadratic equation in the form that has and as its roots.
Write a quadratic equation in the form
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1. Write the equation in the form where and are the given roots.
2. Simplify using FOIL method.
1. Write the equation in the form
2. Simplify using FOIL method.