Quadratic Equations
NIOS · Class 10 · Maths
Flashcards for Quadratic Equations — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedSolve by factorization: x² + 5x + 6 = 0
Answer
Step 1: Find two numbers that multiply to 6 and add to 5 → 2 and 3 Step 2: Factor: (x + 2)(x + 3) = 0 Step 3: Set each factor to zero: x + 2 = 0 or x + 3 = 0 Step 4: Solve: x = -2 or x = -3 Answer: x …
Solve using quadratic formula: 2x² - 7x + 3 = 0
Answer
Step 1: Identify a = 2, b = -7, c = 3 Step 2: Calculate discriminant: D = b² - 4ac = (-7)² - 4(2)(3) = 49 - 24 = 25 Step 3: Apply formula: x = [-(-7) ± √25] / (2×2) = [7 ± 5] / 4 Step 4: Calculate roo…
Without solving, determine the nature of roots: 3x² + 2x + 5 = 0
Answer
Step 1: Identify a = 3, b = 2, c = 5 Step 2: Calculate discriminant: D = b² - 4ac = (2)² - 4(3)(5) = 4 - 60 = -56 Step 3: Since D < 0, the equation has no real roots Answer: No real roots (two complex…
Find the value of k so that x² - 8x + k = 0 has equal roots
Answer
Step 1: For equal roots, discriminant D = 0 Step 2: Here a = 1, b = -8, c = k Step 3: D = b² - 4ac = (-8)² - 4(1)(k) = 64 - 4k Step 4: Set D = 0: 64 - 4k = 0 Step 5: Solve: 4k = 64 → k = 16 Answer: k …
Solve by completing the square: x² + 6x - 7 = 0
Answer
Step 1: Move constant to RHS: x² + 6x = 7 Step 2: Add (6/2)² = 9 to both sides: x² + 6x + 9 = 7 + 9 Step 3: Factor LHS: (x + 3)² = 16 Step 4: Take square root: x + 3 = ±4 Step 5: Solve: x = -3 + 4 = 1…
Solve: (x + 3)(x - 2) = 6
Answer
Step 1: Expand LHS: x² + 3x - 2x - 6 = x² + x - 6 Step 2: Set up equation: x² + x - 6 = 6 Step 3: Rearrange: x² + x - 12 = 0 Step 4: Factor: Find numbers that multiply to -12 and add to 1 → 4 and -3 S…
The sum of two numbers is 12 and their product is 35. Find the numbers.
Answer
Step 1: Let numbers be x and (12-x) Step 2: Product condition: x(12-x) = 35 Step 3: Expand: 12x - x² = 35 Step 4: Rearrange: x² - 12x + 35 = 0 Step 5: Factor: (x - 5)(x - 7) = 0 Step 6: Solve: x = 5 o…
Solve: 6x² + x - 15 = 0 by factorization
Answer
Step 1: Find factors of ac = 6×(-15) = -90 that add to b = 1 Step 2: Factors are 10 and -9 (since 10 + (-9) = 1 and 10×(-9) = -90) Step 3: Split middle term: 6x² + 10x - 9x - 15 = 0 Step 4: Group: 2x(…
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