To determine the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] in the quadratic equation [tex]\( 8x^2 + 5x + 2 = 0 \)[/tex], we must identify the coefficients of the terms in the standard form of a quadratic equation, which is given by:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Here, we need to match the given quadratic equation [tex]\( 8x^2 + 5x + 2 = 0 \)[/tex] to the standard form [tex]\( ax^2 + bx + c \)[/tex].
Observing the given quadratic equation:
1. The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( 8 \)[/tex], so [tex]\( a = 8 \)[/tex].
2. The coefficient of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex], so [tex]\( b = 5 \)[/tex].
3. The constant term is [tex]\( 2 \)[/tex], so [tex]\( c = 2 \)[/tex].
Thus, the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] for the quadratic equation [tex]\( 8x^2 + 5x + 2 = 0 \)[/tex] are:
[tex]\[ a = 8, \, b = 5, \, c = 2 \][/tex]
The correct option is:
[tex]\[ a = 8, \, b = 5, \, c = 2 \][/tex]
