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Identifying the values [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is the first step in using the quadratic formula to find the solution(s) to a quadratic equation.

What are the values of [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] in the following quadratic equation?

[tex]\[ -5x^2 - 9x + 12 = 0 \][/tex]

A. [tex]a=-9[/tex], [tex]b=12[/tex], [tex]c=0[/tex]
B. [tex]a=-5[/tex], [tex]b=-9[/tex], [tex]c=12[/tex]
C. [tex]a=5[/tex], [tex]b=9[/tex], [tex]c=12[/tex]
D. [tex]a=9[/tex], [tex]b=12[/tex], [tex]c=0[/tex]



Answer :

GinnyAnswer
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]

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