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Quadratic Equations — Flashcards

ICSE · Class 11 · Mathematics

25 flashcards for Quadratic Equations (ICSE Class 11 Mathematics) to test yourself on key terms and facts. Sample: "Solve: x^2 - 5x + 6 = 0"

104 questions25 flashcards24 formulas & key relations5 concepts

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An infographic explaining how the discriminant (D = b²-4ac) determines the nature of roots for a quadratic equation ax²+bx+c=0 with real coefficients, including graphical interpretations.
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25 Flashcards·
Solving quadratic equations by factoringQuadratic formulaChoosing a methodDiscriminant and nature of rootsReal irrational rootsIrrational roots with irrational coefficientsComplex coefficient equationsConjugate roots
Card 1Solving quadratic equations by factoring

Solve: x^2 - 5x + 6 = 0

Answer

Step 1: Find two numbers with product 6 and sum -5. Step 2: Write x^2 - 5x + 6 = (x - 2)(x - 3). Step 3: Set each factor equal to zero. (x - 2) = 0 or (x - 3) = 0 Step 4: x = 2 or x = 3 Answer: The ro…

Card 2Quadratic formula

Solve: x^2 + x + 1 = 0 using the quadratic formula

Answer

Step 1: Identify a = 1, b = 1, c = 1. Step 2: Use x = (-b ± √(b^2 - 4ac)) / (2a). Step 3: Substitute values. x = (-1 ± √(1 - 4)) / 2 x = (-1 ± √(-3)) / 2 Step 4: Write √(-3) = i√3. x = (-1 ± i√3) / 2 …

Card 3Choosing a method

When do you use the quadratic formula? Solve x^2 + 8 = 0 as an example.

Answer

Use the quadratic formula when factoring is difficult or not possible. Step 1: Write the equation in ax^2 + bx + c = 0 form. x^2 + 8 = 0 → a = 1, b = 0, c = 8 Step 2: Apply x = (-b ± √(b^2 - 4ac)) / (…

Card 4Discriminant and nature of roots

Find the discriminant of x^2 - 6x + 8 = 0 and state the nature of the roots

Answer

Step 1: Identify a = 1, b = -6, c = 8. Step 2: Use D = b^2 - 4ac. D = (-6)^2 - 4(1)(8) D = 36 - 32 D = 4 Step 3: Since D > 0, the roots are real and distinct. Answer: D = 4, so the roots are real and …

Card 5Real irrational roots

Find the roots of x^2 - 2x - 2 = 0 and classify them

Answer

Step 1: a = 1, b = -2, c = -2. Step 2: Find the discriminant. D = (-2)^2 - 4(1)(-2) = 4 + 8 = 12 Step 3: Since D > 0 and 12 is not a perfect square, the roots are real, irrational, and conjugate. Step…

Card 6Irrational roots with irrational coefficients

Find the roots of x^2 - (5 + √2)x + 5√2 = 0

Answer

Step 1: a = 1, b = -(5 + √2), c = 5√2. Step 2: Use the quadratic formula. x = [5 + √2 ± √((5 + √2)^2 - 20√2)] / 2 Step 3: Simplify the discriminant. (5 + √2)^2 = 25 + 10√2 + 2 = 27 + 10√2 27 + 10√2 - …

Card 7Complex coefficient equations

Solve: x^2 - 2ix - 1 = 0

Answer

Step 1: a = 1, b = -2i, c = -1. Step 2: Use the quadratic formula. x = [2i ± √((-2i)^2 - 4(1)(-1))] / 2 Step 3: Simplify inside the root. (-2i)^2 = -4 -4 + 4 = 0 Step 4: Therefore both roots are equal…

Card 8Conjugate roots

Why do complex roots of a real-coefficient quadratic occur in pairs? Show with an example.

Answer

For a quadratic with real coefficients, if one complex root is a + bi, the other is a - bi. Reason: the non-real part must cancel to keep the coefficients real. Example: x^2 + x + 1 = 0 has roots (-1 …

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Frequently Asked Questions

What are the important topics in Quadratic Equations for ICSE Class 11 Mathematics?
Key topics in Quadratic Equations include Basic Meaning and Standard Form, Discriminant and Nature of Roots, Graph of a Quadratic Function, Roots and Coefficients. Study these first, then practise questions on each for Class 11 exams.
How many flashcards are available for Quadratic Equations?
There are 25 flashcards for Quadratic Equations covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Quadratic Equations for Class 11 exams?
Learn the core ideas first, then work through the 104 practice questions on Quadratic Equations. Revise definitions regularly and use flashcards for quick recall before the exam.

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