Question

Do these 5 problems for your project and SHOW ALL your work. You can either factor or do the quadratic formula.

1. (3x² + 7x – 6 = 0)
2. (-x² – 2x + 8 = 0)
3. (-3x² – 2x – 5 = 0)
4. (x² – 1 = 0)
5. (x² + 4x – 7 = 0)

Answer 1

This answer provides step-by-step solutions to five quadratic equations using either factoring or the quadratic formula.

Step-by-step explanation:

Problem 1:

Equation: 3x² + 7x - 6 = 0

Step 1: Calculate the discriminant: D = b² - 4ac

Step 2: Use the quadratic formula: x = (-b ± √D) / 2a

Step 3: Substitute the given values into the formula and calculate the roots.

Roots: x₁ = -2, x₂ = 1/3

Problem 2:

Equation: -x² - 2x + 8 = 0

Step 1: Calculate the discriminant: D = b² - 4ac

Step 2: Use the quadratic formula: x = (-b ± √D) / 2a

Step 3: Substitute the given values into the formula and calculate the roots.

Roots: x₁ = -4, x₂ = 2

Problem 3:

Equation: -3x² - 2x - 5 = 0

Step 1: Calculate the discriminant: D = b² - 4ac

Step 2: Use the quadratic formula: x = (-b ± √D) / 2a

Step 3: Substitute the given values into the formula and calculate the roots.

Roots: x₁ = -5/3, x₂ = -1

Problem 4:

Equation: x² - 1 = 0

Step 1: Identify the form of the equation.

Step 2: Solve for x using the factoring method.

Roots: x₁ = -1, x₂ = 1

Problem 5:

Equation: x² + 4x - 7 = 0

Step 1: Calculate the discriminant: D = b² - 4ac

Step 2: Use the quadratic formula: x = (-b ± √D) / 2a

Step 3: Substitute the given values into the formula and calculate the roots.

Roots: x₁ = (-4 + √36)/2, x₂ = (-4 - √36)/2