Second Degree Equations — Flashcards
Kerala Board · Class 10 · Mathematics
20 flashcards for Second Degree Equations (Kerala Board Class 10 Mathematics) to test yourself on key terms and facts.
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What is the algebraic identity for completing the square with coefficient 2a?
Answer
x² + 2ax + a² = (x + a)² This identity is fundamental for completing the square. The key is to identify the coefficient of x (which is 2a), divide by 2 to get 'a', then add a² to complete the perfect…
Solve: x² + 6x = 16 using square completion method
Answer
Step 1: Identify the coefficient of x: 6 Step 2: Divide by 2: 6 ÷ 2 = 3 Step 3: Square this value: 3² = 9 Step 4: Add 9 to both sides: x² + 6x + 9 = 16 + 9 Step 5: Factor left side: (x + 3)² = 2…
A rectangle has one side 3 metres longer than the other, and its area is 180 square metres. Set up the equation.
Answer
Let x = length of shorter side (in metres) Then: longer side = x + 3 metres Area = length × breadth 180 = x(x + 3) 180 = x² + 3x Rearranging: x² + 3x - 180 = 0 This is the quadratic equation to sol…
Solve the rectangle problem: x² + 3x = 180
Answer
Step 1: Complete the square Coefficient of x = 3, so add (3/2)² = 9/4 x² + 3x + 9/4 = 180 + 9/4 x² + 3x + 9/4 = 720/4 + 9/4 = 729/4 Step 2: Factor left side (x + 3/2)² = 729/4 Step 3: Ta…
Why do quadratic equations have two solutions?
Answer
When we solve (x - a)² = b², we get: x - a = ±√(b²) = ±b This gives us two cases: 1. x - a = +b, so x = a + b 2. x - a = -b, so x = a - b Geometrically, a parabola (graph of quadratic equation) inte…
A square's side was extended by 2 metres and the new area became 144 square metres. Find the original side length.
Answer
Let x = original side length New side length = x + 2 New area = (x + 2)² = 144 Step 1: Take square root x + 2 = ±12 Step 2: Solve for x x = 12 - 2 = 10 or x = -12 - 2 = -14 Step 3: Choose v…
What number should be added to x² - 8x to make it a perfect square?
Answer
To complete the square for x² - 8x: Step 1: Identify coefficient of x: -8 Step 2: Divide by 2: -8 ÷ 2 = -4 Step 3: Square this value: (-4)² = 16 Therefore, add 16 to get: x² - 8x + 16 = (x - 4)² Th…
The product of two consecutive even numbers is 288. Find the numbers.
Answer
Let the two consecutive even numbers be x and x + 2 Step 1: Set up equation x(x + 2) = 288 x² + 2x = 288 Step 2: Complete the square x² + 2x + 1 = 288 + 1 = 289 (x + 1)² = 289 Step 3: S…
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
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