First, let's recall the general form of a quadratic equation:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
In this equation:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex],
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex], and
- [tex]\( c \)[/tex] is the constant term.
Now let's compare this with the given quadratic equation:
[tex]\[ -5x^2 - 9x + 12 = 0 \][/tex]
By directly comparing terms in the equation, we can identify the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
- The coefficient of [tex]\( x^2 \)[/tex] (which is [tex]\( a \)[/tex]) is [tex]\(-5\)[/tex],
- The coefficient of [tex]\( x \)[/tex] (which is [tex]\( b \)[/tex]) is [tex]\(-9\)[/tex],
- The constant term (which is [tex]\( c \)[/tex]) is [tex]\( 12 \)[/tex].
Therefore, the correct values are:
- [tex]\( a = -5 \)[/tex],
- [tex]\( b = -9 \)[/tex],
- [tex]\( c = 12 \)[/tex].
This corresponds to the option:
[tex]\[ a = -5,\ b = -9,\ c = 12 \][/tex]
So the correct answer is:
[tex]\[ a = -5, \ b = -9, \ c = 12 \][/tex]
