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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 [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] in the following quadratic equation?

[tex]\[ -3x^2 - 5x + 9 = 0 \][/tex]

A. [tex]a = 5, b = 9, c = 0[/tex]

B. [tex]a = 3, b = 5, c = 9[/tex]

C. [tex]a = -3, b = -5, c = 9[/tex]

D. [tex]a = -5, b = 9, c = 0[/tex]

Sagot :

GinnyAnsweridn
To identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the quadratic equation [tex]\(-3x^2 - 5x + 9 = 0\)[/tex], we need to compare it to the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex].

Given the equation:

[tex]\[ -3x^2 - 5x + 9 = 0 \][/tex]

We can identify the coefficients as follows:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(a\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(b\)[/tex].
- The constant term is [tex]\(c\)[/tex].

Therefore, by comparing:

- For [tex]\(a\)[/tex], we have the coefficient of [tex]\(x^2\)[/tex], which is [tex]\(-3\)[/tex].
- For [tex]\(b\)[/tex], we have the coefficient of [tex]\(x\)[/tex], which is [tex]\(-5\)[/tex].
- For [tex]\(c\)[/tex], we have the constant term, which is [tex]\(9\)[/tex].

Thus, the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are:
[tex]\[ a = -3, \][/tex]
[tex]\[ b = -5, \][/tex]
[tex]\[ c = 9. \][/tex]

This matches the option:
[tex]\[ a = -3, b = -5, c = 9. \][/tex]
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