QuestionWhich statements about quadratic equations are true? I. The form is , . II. All quadratics can be linear. A. I only B. II only C. III only D. I and II
Studdy Solution
STEP 1
Assumptions1. The quadratic equation is given in the form where are real numbers and .
. The roots of a quadratic equation are not always rational numbers.
3. Not all quadratic equations can be linear equations.
STEP 2
Let's analyze each statement one by one.
Statement I The roots of a quadratic equation are always rational numbers.
This statement is false. The roots of a quadratic equation can be irrational or even complex numbers. For example, the quadratic equation has roots that are imaginary numbers.
STEP 3
Statement II The form of a quadratic equation is denoted by where are real numbers and .
This statement is true. This is the standard form of a quadratic equation.
STEP 4
Statement III All quadratic equations can be linear equations.
This statement is false. Quadratic equations and linear equations are fundamentally different. A quadratic equation involves the square of the variable, whereas a linear equation does not.
STEP 5
Based on the analysis, the correct answer is B. II only.
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