Question

Use the Information provided to answer Part A and Part B for question 2. lel a represent a non-zera rational number and let b represent an irrational number Part A Which expression could represent a rational number? DE PEFETE Consider a quadratie equation with integer coefficients and two distinct zeros. one zere is ifrational, which staternent is true about the other zero? A The other tere must be rational, B. The other zero must be irracional. c. The emergerouar berleher rational or irrational. De ezero US Del Peel,

Answer 1

For part A, the only possible option that could represent a rational number is

`b^2`

Because all the other options are irrational numbers.

For part B, the other zero has to be irrational too. To prove this we use the general formula for quadratic equations:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}`

If x1 is an irrational number, then

`\sqrt[]{b^2-4ac}\text{ }`