Quadratic Equations — Flashcards
Punjab Board · Class 10 · Mathematics
25 flashcards for Quadratic Equations (Punjab Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve: x² - 5x + 6 = 0 by factorization
Answer
Step 1: Find two numbers that multiply to 6 and add to -5 → -2 and -3 Step 2: Split middle term: x² - 2x - 3x + 6 = 0 Step 3: Factor by grouping: x(x - 2) - 3(x - 2) = 0 Step 4: Factor out common term…
Solve: 2x² - 7x + 3 = 0 by factorization
Answer
Step 1: We need two numbers that multiply to (2)(3) = 6 and add to -7 → -6 and -1 Step 2: Rewrite: 2x² - 6x - x + 3 = 0 Step 3: Factor by grouping: 2x(x - 3) - 1(x - 3) = 0 Step 4: Extract common fact…
When do you use the quadratic formula? Give the formula and an example where factorization is difficult.
Answer
Use when: Factorization is difficult or impossible, or when roots are irrational/complex. Formula: x = [-b ± √(b² - 4ac)] / 2a Where: a = coefficient of x², b = coefficient of x, c = constant term …
Is (x - 2)² + 1 = 2x - 3 a quadratic equation? Show your work.
Answer
Step 1: Expand LHS: (x - 2)² + 1 = x² - 4x + 4 + 1 = x² - 4x + 5 Step 2: Rewrite equation: x² - 4x + 5 = 2x - 3 Step 3: Move all terms to LHS: x² - 4x - 2x + 5 + 3 = 0 Step 4: Simplify: x² - 6x + 8 = …
A rectangular garden has area 300 m². Its length is one meter more than twice its breadth. Form a quadratic equation and find dimensions.
Answer
Step 1: Let breadth = x m, then length = (2x + 1) m Step 2: Form equation: x(2x + 1) = 300 Step 3: Expand: 2x² + x = 300 Step 4: Standard form: 2x² + x - 300 = 0 Step 5: Factorize by splitting middle …
Formula for discriminant. What does each discriminant value tell us?
Answer
Discriminant Formula: Δ = b² - 4ac Where: a = coefficient of x², b = coefficient of x, c = constant What it tells us: 1) If Δ > 0: Two distinct real roots Example: x² - 5x + 6 = 0 Δ = (-5)² -…
Find discriminant and nature of roots for 2x² - 4x + 3 = 0
Answer
Step 1: Identify coefficients: a = 2, b = -4, c = 3 Step 2: Calculate discriminant: Δ = b² - 4ac Δ = (-4)² - 4(2)(3) Δ = 16 - 24 Δ = -8 Step 3: Interpret result: Since …
Solve: x² - 8x + 15 = 0 using two different methods. Show both.
Answer
METHOD 1: FACTORIZATION Step 1: Find factors of 15 that add to -8 → -3 and -5 Step 2: Rewrite: x² - 3x - 5x + 15 = 0 Step 3: Factor: x(x - 3) - 5(x - 3) = 0 Step 4: Simplify: (x - 3)(x - 5) = 0 Step 5…
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