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
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 |
Part A
Take, for example, a = 3 as a rational number, and b = √7 as an irrational number. A.) -b, would be -√7 {irrational} B.) a + b would be 3 + √7 {irrational} C.) ab would be 3√7 {irrational} D.) b² would be (√7)² which would be 7 {rational} Ask Algebra House |
Part B
A zero of a quadratic equation is a "solution" or "x-intercept" of the graph. If one zero is irrational, that means one x-intercept or "solution" is imaginary. On the graph of a parabola, if one x-intercept is imaginary, then the other would also be imaginary. Therefore, the other zero must be irrational. B.) |