Polynomials — Flashcards
Gujarat Board · Class 10 · Mathematics
28 flashcards for Polynomials (Gujarat Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Identify the degree and type.
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Identify the degree and type of polynomial: 3x² + 5x - 2
Answer
Step 1: Look at the highest power of x in the polynomial → x² is the highest power Step 2: Degree = 2 Step 3: A polynomial of degree 2 is called a quadratic polynomial Answer: Degree = 2, Type = Quadr…
Is 5/x + 3x - 2 a polynomial? Justify your answer.
Answer
Step 1: Check each term in the expression - First term: 5/x = 5x⁻¹ (has negative exponent) - Second term: 3x (positive integer exponent ✓) - Third term: -2 (constant term ✓) Step 2: Polynomials …
Classify by degree: (i) 7y + 4 (ii) 2x³ - 5x + 1 (iii) 8 (iv) √2u⁴ + 3u² - 5
Answer
Step 1: Find highest power of variable in each (i) 7y + 4: Highest power is y¹ → Degree = 1 → Linear polynomial (ii) 2x³ - 5x + 1: Highest power is x³ → Degree = 3 → Cubic polynomial (iii) 8: Co…
Find the value of p(x) = x² - 3x - 4 at x = -1 and x = 4
Answer
Step 1: Find p(-1) p(-1) = (-1)² - 3(-1) - 4 = 1 + 3 - 4 = 0 Step 2: Find p(4) p(4) = (4)² - 3(4) - 4 = 16 - 12 - 4 = 0 Answer: p(-1) = 0 and p(4) = 0 Important: When p(k) = 0, we say k is…
When do we call a number 'a zero of a polynomial'? Give an example.
Answer
Definition: A real number k is a zero of polynomial p(x) if p(k) = 0 Example: For p(x) = x² - 5x + 6 Step 1: Test x = 2 → p(2) = 4 - 10 + 6 = 0 ✓ Step 2: Test x = 3 → p(3) = 9 - 15 + 6 = 0 ✓ Answer: B…
Find the zero of linear polynomial: 2x + 3
Answer
Step 1: Set the polynomial equal to zero 2x + 3 = 0 Step 2: Solve for x 2x = -3 x = -3/2 Step 3: Verify: p(-3/2) = 2(-3/2) + 3 = -3 + 3 = 0 ✓ Answer: The zero is -3/2 Formula: For ax + b, zero =…
Apply the formula to find zeroes of: 5x - 7 = 0
Answer
Method 1: Using formula For polynomial 5x - 7 (where a = 5, b = -7) Zero = -b/a = -(-7)/5 = 7/5 Method 2: Solving directly 5x - 7 = 0 5x = 7 x = 7/5 Step 3: Verify: 5(7/5) - 7 = 7 - 7 = 0 …
Factorise 2x² - 8x + 6 and find its zeroes
Answer
Step 1: Factor out common factor 2x² - 8x + 6 = 2(x² - 4x + 3) Step 2: Split middle term of x² - 4x + 3 Need two numbers: multiply to 3, add to -4 → (-1) and (-3) x² - 4x + 3 = x² - x - 3x + 3 …
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