Solving Quadratic Equations with Binary Operator $\otimes$

  • MHB
  • Thread starter karush
  • Start date
In summary, the binary operator $\otimes$ is defined as $a\otimes b = a^2+b+9$. The results for the given inputs are: a) $6\otimes 4 = 49$, b) $3\otimes 3 = 21$, c) $4\otimes 6 = 31$, and d) $i\otimes p = i^2+p+9$. It is recommended to use a programming language, such as Python, to check for any arithmetic errors.
  • #1
karush
Gold Member
MHB
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5
Define the binary operater $\otimes$ by
$a\otimes b = a^2+b+9$
Find
a. $6\otimes 4 = 6^2+4+9 = 36+13 = 49$
b. $3\otimes 3 = 3^2+3+9 = 9+13 = 22$
c $4\otimes 6 = 4^2+6+9 = 16+15 =21$
d. $i\otimes p = i^2+p+9$

i think its ok but most math errors are in simple arithmetic
 
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  • #2
b and c have arithmetic errors.

The best way to check the answers is to write a function in some programming language and run it on your inputs. For example, in Python the function would be
Python:
def f(x, y):
  return x**2 + y + 9
Then you can run f(6, 4) and so on in an interpreter.
 
  • #3
karush said:
Define the binary operater $\otimes$ by
$a\otimes b = a^2+b+9$
Find
a. $6\otimes 4 = 6^2+4+9 = 36+13 = 49$
b. $3\otimes 3 = 3^2+3+9 = 9+13 = 22$
c $4\otimes 6 = 4^2+6+9 = 16+15 =21$
d. $i\otimes p = i^2+p+9$

i think its ok but most math errors are in simple arithmetic
Evgeny.Makarov said:
b and c have arithmetic errors.

The best way to check the answers is to write a function in some programming language and run it on your inputs. For example, in Python the function would be
Python:
def f(x, y):
  return x**2 + y + 9
Then you can run f(6, 4) and so on in an interpreter.
Evgeny.Makarov said:
b and c have arithmetic errors.

The best way to check the answers is to write a function in some programming language and run it on your inputs. For example, in Python the function would be
Python:
def f(x, y):
  return x**2 + y + 9
Then you can run f(6, 4) and so on in an interpreter.
ummm is that under colcalc
at least I saw it there when one class was teaching us the programs
 
  • #4
Python is a programming language that can be used in different environments: CoCalc, Jupyter Notebook, PyCharm by JetBrains or simply from the command line. Use whatever tool you are familiar with, or use any other programming language.

It's a good idea to quote only relevant passages.
 
  • #5
Find (corrected)
a. $6\otimes 4 = 6^2+4+9 = 36+13 = 49$
b. $3\otimes 3 = 3^2+3+9 = 9+13 = 21$
c $4\otimes 6 = 4^2+6+9 = 16+15 =31$
d. $i\otimes p = i^2+p+9$
 
  • #6
$3^2+3+9=9+12$.
 
  • #7
gotcha
3\otimes 3 = 3^2+3+9 = 9+12= 21
 

Related to Solving Quadratic Equations with Binary Operator $\otimes$

1. What is a quadratic equation?

A quadratic equation is a mathematical equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is called a quadratic equation because the highest power of x is 2.

2. What is a binary operator?

A binary operator is a mathematical symbol or function that takes two operands and performs a specific operation on them. In the context of solving quadratic equations, the binary operator $\otimes$ represents the operation of combining two numbers or expressions using a specific rule.

3. How do you solve a quadratic equation using the binary operator $\otimes$?

To solve a quadratic equation using the binary operator $\otimes$, you first need to rewrite the equation in the form of (ax $\otimes$ bx) + c = 0. Then, you can use the properties of the binary operator $\otimes$ to isolate the variable and solve for its value.

4. What are some common examples of binary operators?

Some common examples of binary operators include addition (+), subtraction (-), multiplication (*), and division (/). Other examples include exponentiation (^), modulus (%), and logarithms (log).

5. Can the binary operator $\otimes$ be used to solve all types of quadratic equations?

No, the binary operator $\otimes$ is a specific operator that may not be applicable to all types of quadratic equations. It is important to carefully analyze the equation and determine if the binary operator $\otimes$ can be used to solve it effectively.

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