Alright, let's proceed step-by-step to fill in the values for the given quadratic equation [tex]\(-3x^2 + 4x + 1 = 0\)[/tex].
1. Identifying coefficients:
For the quadratic equation of the form [tex]\(ax^2 + bx + c = 0\)[/tex]:
- [tex]\(a = -3\)[/tex]
- [tex]\(b = 4\)[/tex]
- [tex]\(c = 1\)[/tex]
2. Substituting coefficients into the quadratic formula:
The quadratic formula is given by:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
Substituting the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula:
[tex]\[
x = \frac{-4 \pm \sqrt{4^2 - 4(-3)(1)}}{2(-3)}
\][/tex]
So, the values we should enter are:
[tex]\( a = -3 \)[/tex]
[tex]\( b = 4 \)[/tex]
[tex]\( c = 1 \)[/tex]
Thus, the quadratic formula becomes:
[tex]\[
x = \frac{-4 \pm \sqrt{4^2 - 4(-3)(1)}}{2(-3)}
\][/tex]
