Quadratic Equations — Important Questions

Factorization method, Quadratic formula, Completing the square

The three main methods to solve quadratic equations are: 1) Factorization method - expressing as product of linear factors, 2) Quadratic formula - using x = (-b ± √(b²-4ac))/2a, 3) Completing the square - making a perfect square trinomial. Cross multiplication and linear substitution are not methods for solving quadratic equations.

Real and equal

Step 1: Identify a = 1, b = 4, c = 4. Step 2: Calculate discriminant: Δ = b² - 4ac = 16 - 4(1)(4) = 16 - 16 = 0. Step 3: Since Δ = 0, roots are real and equal.

2/5

Step 1: For equation ax² + bx + c = 0, product of roots = c/a. Step 2: Here a = 5, c = 2. Step 3: Product of roots = c/a = 2/5.

x = ±3

Step 1: Recognize as difference of squares: x² - 9 = x² - 3². Step 2: Factor: (x + 3)(x - 3) = 0. Step 3: Set each factor to zero: x + 3 = 0 or x - 3 = 0. Step 4: Solve: x = -3 or x = 3.