Sure, let's solve the quadratic equation [tex]\(5 - 3x = 2x^2\)[/tex] and find out who has the correct values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[ 5 - 3x = 2x^2 \][/tex]
2. Rearrange the terms to get the equation in standard quadratic form [tex]\( ax^2 + bx + c = 0 \)[/tex]:
[tex]\[ 2x^2 + 3x - 5 = 0 \][/tex]
3. Compare this with the general quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex]:
- Here, [tex]\(a = 2\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -5\)[/tex]
These are the coefficients for the quadratic equation when rewritten in standard form.
### Checking the Students' Values:
- Student A reported: [tex]\(a = 2\)[/tex], [tex]\(b = 3\)[/tex], [tex]\(c = -5\)[/tex]
- Student B reported: [tex]\(a = -2\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex] as [tex]\(-3\)[/tex], [tex]\(6\)[/tex], [tex]\(5\)[/tex] (Note that Student B’s values seem incorrectly formatted).
### Analysis of Students' Values:
- Student A's values are [tex]\(a = 2\)[/tex], [tex]\(b = 3\)[/tex], [tex]\(c = -5\)[/tex], which exactly match our derived values.
- Student B's values are incorrectly formatted and do not correspond to a coherent set of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] for the equation in standard form.
### Conclusion:
- Student A has the correct values. The correct coefficients for the quadratic equation [tex]\(5 - 3x = 2x^2\)[/tex] transformed into standard form [tex]\(2x^2 + 3x - 5 = 0\)[/tex] are [tex]\(a = 2\)[/tex], [tex]\(b = 3\)[/tex], and [tex]\(c = -5\)[/tex].
Therefore, Student A got the correct values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
