Part A
Which expression could represent a rational number? A.) -b B.) a + b C.) ab D.) b² |
Part B
Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A.) The other zero must be rational. B.) The other zero must be irrational. C.) The other zero can be either rational or irrational. D.) The other zero must be non-real. |
Use the information provided to answer Part A and Part B.
Let a represent a non-zero rational number and let b represent an irrational number.
Let a represent a non-zero rational number and let b represent an irrational number.
Part A
A rational number is any number that can be written as a ratio of two integers (in the form of a fraction).
An irrational number, such as √2, when squared, would become rational. Such as (√2)² = 2. Since 2 can be written as a fraction, as in 2/1.
Answer is D.) b²
About the other answers:
A.) b would obviously be irrational.
B.) a + b would be irrational, since nothing is done to make the irrational portion, b, become rational.
C.) ab would be irrational, since nothing is done to make the irrational portion, b, become rational.
A rational number is any number that can be written as a ratio of two integers (in the form of a fraction).
An irrational number, such as √2, when squared, would become rational. Such as (√2)² = 2. Since 2 can be written as a fraction, as in 2/1.
Answer is D.) b²
About the other answers:
A.) b would obviously be irrational.
B.) a + b would be irrational, since nothing is done to make the irrational portion, b, become rational.
C.) ab would be irrational, since nothing is done to make the irrational portion, b, become rational.
Part B
Zeros of a quadratic equation are also known as "solutions", "roots", or "x-intercepts".
If one zero is irrational, the other must also be irrational.
Answer is B.) The other zero must be irrational.
Based on the discriminant, b² - 4ac (the portion under the radical sign within the quadratic formula):
If the discriminant is positive and a perfect square, there will be two real rational solutions.
If the discriminant is positive and not a perfect square, there will be two real irrational solutions.
If the discriminant is negative, there will be two imaginary solutions.
If the discriminant is zero, there will be one real solution.
- Algebra House
Zeros of a quadratic equation are also known as "solutions", "roots", or "x-intercepts".
If one zero is irrational, the other must also be irrational.
Answer is B.) The other zero must be irrational.
Based on the discriminant, b² - 4ac (the portion under the radical sign within the quadratic formula):
If the discriminant is positive and a perfect square, there will be two real rational solutions.
If the discriminant is positive and not a perfect square, there will be two real irrational solutions.
If the discriminant is negative, there will be two imaginary solutions.
If the discriminant is zero, there will be one real solution.
- Algebra House