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Quadratic Equations and Linear Inequalities

NIOS · Class 12 · Mathematics

Flashcards for Quadratic Equations and Linear Inequalities — NIOS Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

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25 Flashcards
Card 1Solving Quadratic Equations by Factorization

Solve the quadratic equation: 6x² + 5x - 6 = 0 using factorization method

Answer

Step 1: Write the equation: 6x² + 5x - 6 = 0 Step 2: Split middle term 5x into two parts whose product = 6 × (-6) = -36 and sum = 5. Use +9x and -4x Step 3: 6x² + 9x - 4x - 6 = 0 Step 4: Factor by gro…

Card 2Quadratic Formula Application

When should you use the Quadratic Formula instead of factorization? Give an example where factorization is difficult.

Answer

Use the Quadratic Formula when: (1) The quadratic expression doesn't factor easily over integers, (2) Coefficients are large, (3) Roots are irrational or complex, (4) You need to verify the nature of …

Card 3Nature of Roots Using Discriminant

Find the discriminant and nature of roots for: 9y² - 6√2y + 2 = 0

Answer

Step 1: Identify coefficients: a = 9, b = -6√2, c = 2 Step 2: Apply discriminant formula D = b² - 4ac Step 3: D = (-6√2)² - 4(9)(2) Step 4: D = 36(2) - 72 = 72 - 72 = 0 Step 5: Since D = 0, the equati…

Card 4Relation Between Roots and Coefficients

What is the relationship between the roots (α, β) and coefficients (a, b, c) of ax² + bx + c = 0? Give a quick example.

Answer

Relationships (Vieta's Formulas): (1) Sum of roots: α + β = -b/a (2) Product of roots: αβ = c/a Example: For 3x² - 5x + 9 = 0 where a=3, b=-5, c=9: α + β = -(-5)/3 = 5/3 αβ = 9/3 = 3 Why it matters:…

Card 5Forming Equations with Transformed Roots

Form a quadratic equation whose roots are α² and β², given that α and β are roots of 3y² + 4y + 1 = 0

Answer

Step 1: From 3y² + 4y + 1 = 0, find sum and product of original roots: α + β = -4/3 αβ = 1/3 Step 2: Calculate new sum (α² + β²): α² + β² = (α + β)² - 2αβ = (-4/3)² - 2(1/3) = 16/9 - 2/3 = 16/9 - 6/9…

Card 6Complex Roots of Quadratic Equations

Solve: √2t² - 3t + 3√2 = 0. Determine the nature of roots WITHOUT solving completely.

Answer

Step 1: Identify coefficients: a = √2, b = -3, c = 3√2 Step 2: Calculate discriminant D = b² - 4ac Step 3: D = (-3)² - 4(√2)(3√2) = 9 - 4(3)(2) = 9 - 24 = -15 Step 4: Since D = -15 < 0, roots are COMP…

Card 7Solving Linear Inequalities in One Variable

Solve the inequality: (3x - 4)/2 ≥ (x + 1)/4 - 1. Show the solution on a number line.

Answer

Step 1: Simplify RHS: (x + 1)/4 - 1 = (x + 1)/4 - 4/4 = (x + 1 - 4)/4 = (x - 3)/4 So inequality becomes: (3x - 4)/2 ≥ (x - 3)/4 Step 2: Multiply both sides by 4 (positive, no sign change): 2(3x - 4) …

Card 8Real-World Applications of Linear Inequalities

A student has marks 62 and 48 in two exams. What minimum marks in the annual exam to get an average of at least 60?

Answer

Step 1: Let x = marks in annual exam Step 2: Set up the inequality for average ≥ 60: (62 + 48 + x)/3 ≥ 60 Step 3: Simplify: (110 + x)/3 ≥ 60 Step 4: Multiply both sides by 3 (positive): 110 + x ≥ 18…

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Frequently Asked Questions

What are the important topics in Quadratic Equations and Linear Inequalities for NIOS Class 12 Mathematics?
Key topics in Quadratic Equations and Linear Inequalities include Mind map showing the structure, components, and key characteristics of a quadratic equation, Step-by-step flowchart showing the factorization method for solving quadratic equations, Flowchart showing the quadratic formula method and how the discriminant determines root nature. These are the concepts NIOS Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Quadratic Equations and Linear Inequalities — NIOS Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many flashcards are available for Quadratic Equations and Linear Inequalities?
There are 25 flashcards for Quadratic Equations and Linear Inequalities covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

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