Formula Finder Answer Key
Answer Key
Formula Finder Worksheet
TEACHER COPY
Q1
x² + 6x + 5 = 0
Coefficients
\(a = 1, b = 6, c = 5\)
Discriminant
\(D = 6^2 - 4(1)(5) = \mathbf{16}\)
Final Solutions
x = -1, x = -5
Work: \( \frac{-6 \pm \sqrt{16}}{2} \rightarrow \frac{-6+4}{2} = -1; \frac{-6-4}{2} = -5 \)
Q2
x² - 8x + 12 = 0
Coefficients
\(a = 1, b = -8, c = 12\)
Discriminant
\(D = (-8)^2 - 4(1)(12) = \mathbf{16}\)
Final Solutions
x = 6, x = 2
Work: \( \frac{8 \pm \sqrt{16}}{2} \rightarrow \frac{8+4}{2} = 6; \frac{8-4}{2} = 2 \)
Q3
2x² - 5x + 3 = 0
Coefficients
\(a = 2, b = -5, c = 3\)
Discriminant
\(D = (-5)^2 - 4(2)(3) = \mathbf{1}\)
Final Solutions
x = 1.5, x = 1
Work: \( \frac{5 \pm \sqrt{1}}{4} \rightarrow \frac{6}{4} = 1.5; \frac{4}{4} = 1 \)
Q4
x² + 4x - 7 = 0
Coefficients
\(a = 1, b = 4, c = -7\)
Discriminant
\(D = 4^2 - 4(1)(-7) = \mathbf{44}\)
Final Solutions
x ≈ 1.32, x ≈ -5.32
Work: \( \frac{-4 \pm \sqrt{44}}{2} \approx \frac{-4 \pm 6.63}{2} \)
