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What expression gives the values of the roots (if any) of the quadratic equation ax? + bx + c = 0 -b± /b² – ac X 1,2 2a b+ vb? – 4ac X1,2 2a b± vb² – ac X1,2 2a -6+ V6? – 4ac X1,2 2a

What expression gives the values of the roots (if any) of the quadratic equation ax? + bx + c = 0 -b± /b² – ac X 1,2 2a b+ vb? – 4ac X1,2 2a b± vb² – ac X1,2 2a -6+ V6? – 4ac X1,2 2a

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
**Quadratic Equation Roots** To determine the values of the roots (if any) for the quadratic equation given by: \[ ax^2 + bx + c = 0 \] Consider the following expressions: 1. \( x_{1,2} = \frac{-b \pm \sqrt{b^2 - ac}}{2a} \) 2. \( x_{1,2} = \frac{b \pm \sqrt{b^2 - 4ac}}{2a} \) 3. \( x_{1,2} = \frac{b \pm \sqrt{b^2 - ac}}{2a} \) 4. \( x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) The correct expression for the roots of the quadratic equation is: \[ x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] This formula is known as the quadratic formula, and it provides the solutions to any quadratic equation, where \( a \), \( b \), and \( c \) are coefficients of the equation, and \( b^2 - 4ac \) is the discriminant. The discriminant determines the nature of the roots: - If \( b^2 - 4ac > 0 \), there are two distinct real roots. - If \( b^2 - 4ac = 0 \), there is exactly one real root (a repeated root). - If \( b^2 - 4ac < 0 \), there are no real roots (the roots are complex).
Transcribed Image Text:**Quadratic Equation Roots** To determine the values of the roots (if any) for the quadratic equation given by: \[ ax^2 + bx + c = 0 \] Consider the following expressions: 1. \( x_{1,2} = \frac{-b \pm \sqrt{b^2 - ac}}{2a} \) 2. \( x_{1,2} = \frac{b \pm \sqrt{b^2 - 4ac}}{2a} \) 3. \( x_{1,2} = \frac{b \pm \sqrt{b^2 - ac}}{2a} \) 4. \( x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) The correct expression for the roots of the quadratic equation is: \[ x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] This formula is known as the quadratic formula, and it provides the solutions to any quadratic equation, where \( a \), \( b \), and \( c \) are coefficients of the equation, and \( b^2 - 4ac \) is the discriminant. The discriminant determines the nature of the roots: - If \( b^2 - 4ac > 0 \), there are two distinct real roots. - If \( b^2 - 4ac = 0 \), there is exactly one real root (a repeated root). - If \( b^2 - 4ac < 0 \), there are no real roots (the roots are complex).
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