1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marina CMI [18]
3 years ago
6

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

Mathematics
1 answer:
tekilochka [14]3 years ago
7 0

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

<u>1. 2x^2 - 7x + 3</u>

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

  • a = 2
  • b = -7
  • c = 3

we can use the quadratic formula: x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}

Substitute the a, b, and c values into the quadratic formula: x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}

Now simplify using the laws of pemdas: x=\frac{7\pm\sqrt{(49)-(24)} }{4}

Simplify even further: x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}

Now split this equation into two equations to solve for x: x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

\boxed {x=3,\frac{1}{2} }

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

  • x - 3 = 0
  • 2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

<u>2. 3x^2 + 7x + 2</u>

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

  • 3x + 1 = 0
  • x + 2 = 0

Solve.

<u>First factor:</u> 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

<u>Second factor:</u> x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

\boxed {x = -\frac{1}{3} , -2}

You might be interested in
Solve for x. Show your work.
hram777 [196]
5(5+x) = 6(6+4)
25+5x = 60
5x = 35
  x = 7

-----------------
3(3+5) = 4(4+x)
24 = 16 + 4x
4x = 24-16
4x = 8
  x = 2

7 0
3 years ago
Read 2 more answers
Which expressions are equivalent to -6+4q+(-6q)
enot [183]

Answer:

c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which statement describes the first step to solve the equation by completing the square?
Readme [11.4K]

Answer:

It's Multiply both sides of the equation by 1/2, I literally just took the quiz.  

6 0
3 years ago
Read 2 more answers
Find the sum or difference. 1 3/10 + 2 2/5
pychu [463]
The answer is 3 7/10
8 0
2 years ago
Read 2 more answers
If D is an n × n diagonal matrix with entries dii, then det D = d11d22 ∙ ∙ ∙ dnn. Verify this theorem for 2 × 2 matrices.
nadya68 [22]

Answer:

Verified

Step-by-step explanation:

Let the diagonal matrix D with size 2x2 be in the form of

\left[\begin{array}{cc}a&0\\0&d\end{array}\right]

Then the determinant of matrix D would be

det(D) = a*d - 0*0 = ad

This is the product of the matrix's diagonal numbers

So the theorem is true for 2x2 matrices

8 0
3 years ago
Other questions:
  • Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc
    12·2 answers
  • How much sale tax would be charged on $450 worth of merchandise if the sales tax rate is 8 3/4%?What is the final cost?
    11·2 answers
  • The area of a rectangle garden is 38 1/4 Square meters the width of the garden is 4 1/2 meters. Find the length of the garden
    9·1 answer
  • Help me please I really needa turn this in by tmr
    8·1 answer
  • This afternoon, Sara noticed that the number of the page assigned for homework is divisible by both 12
    7·1 answer
  • there are 45 students in the six grade at garden valley middle school. nine of them have freckles. what is the ratio 26 graders
    9·2 answers
  • Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Cynthia plans to make the area of her tree house
    11·1 answer
  • 3 times what equal 19?
    7·2 answers
  • The area shaded purple contains the solutions to this system of equations. Which ordered pair is a solution to the system?
    9·1 answer
  • Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of ca
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!