Questions: Using the quadratic formula
Before attempting these questions, it is recommended that you read Guide: Using the quadratic formula.
Q1
Using the quadratic formula or otherwise, solve the following quadratic equations.
1.1. \(\quad x^2 - 7x + 6 = 0\).
1.2. \(\quad x^2 + 14x + 45 = 0\).
1.3. \(\quad x^2 - 4x + 13 = 0\).
1.4. \(\quad x^2 - x - 56 = 0\).
1.5. \(\quad s^2 + 4s + 4 = 0\).
1.6. \(\quad t^2 + 4t - 4 = 0\).
1.7. \(\quad m^2 - 144 = 0\).
1.8. \(\quad 5c^2 - 25 + 30 = 0\).
1.9. \(\quad 2n^2 + n + 1 = 0\).
1.10. \(\quad -3c^2 + 9c - 1 = 0\).
1.11. \(\quad \frac{x^2}{2} - \frac{7x}{2} + 3 = 0\).
1.12. \(\quad e^{2x} - 4e^x + 4 = 0\)
1.13. \(\quad -9s^2 + 3s - 1 = 0\)
1.14. \(\quad 2e^{6x} + e^{3x} + 1 = 0\).
1.15. \(\quad \cos^2(x) + 4\cos(x) - 4 = 0\).
1.16. \(\quad 8m^2 - 4m - 1 = 0\).
Q2
In Questions: Introduction to quadratic equations, you saw that the following expressions are all quadratic equations in disguise. Solve these for the variable indicated.
2.1. \(\quad x = 1/x - 1\); solve for \(x\).
2.2. \(\quad (y-1)(y-4) = -(y+2)(y+3)\); solve for \(y\).
2.3. \(\quad 4m(m+1) + 6 = 5\); solve for \(m\).
2.4. \(\quad (t-1)(t+1) = -2\); solve for \(t\).
2.5. \(\quad \displaystyle \frac{x-1}{x-2} = 5x\); solve for \(x\).
2.6. \(\quad \displaystyle \frac{e^{x} - e^{-x}}{2} = 1\); solve for \(x\) (you may need Guide: Introduction to logarithms to express your answers.)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 04/23 by tdhc.
- v1.1: edited 05/24 by tdhc.