Certainly! Let's break down the given quadratic equation step-by-step.
Given quadratic equation:
[tex]\[ 3x^2 - 2x + 1 = 0 \][/tex]
Here is how we identify each part of the quadratic equation:
1. Identify the coefficient of [tex]\( x^2 \)[/tex]:
The term associated with [tex]\( x^2 \)[/tex] is [tex]\( 3x^2 \)[/tex].
[tex]\[
a = 3
\][/tex]
2. Identify the coefficient of [tex]\( x \)[/tex]:
The term associated with [tex]\( x \)[/tex] is [tex]\( -2x \)[/tex].
[tex]\[
b = -2
\][/tex]
3. Identify the constant term:
The constant term (term without [tex]\( x \)[/tex]) is [tex]\( 1 \)[/tex].
[tex]\[
c = 1
\][/tex]
So, for the given quadratic equation [tex]\( 3x^2 - 2x + 1 = 0 \)[/tex], the coefficients are:
[tex]\[ a = 3, \; b = -2, \; c = 1 \][/tex]
To summarize:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( 3x^2 \)[/tex], which is [tex]\( 3 \)[/tex].
- [tex]\( b \)[/tex] is the coefficient of [tex]\( -2x \)[/tex], which is [tex]\( -2 \)[/tex].
- [tex]\( c \)[/tex] is the constant term, which is [tex]\( 1 \)[/tex].
These values can be directly read off from the quadratic equation in the standard form [tex]\( ax^2 + bx + c = 0 \)[/tex].
Thus, the coefficients are [tex]\( a = 3 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 1 \)[/tex].
