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)
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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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![**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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2810685e-1eeb-461a-9149-0ef27d84930f%2Fcaf03bae-1323-4be8-8146-5c4bb35340de%2Fvak5wo7_processed.png&w=3840&q=75)
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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