Polynomials — Important Questions
Gujarat Board · Class 9 · Mathematics
45 important questions from Polynomials for Gujarat Board Class 9 Mathematics, with answers. Part of the Gujarat Board Class 9 Mathematics syllabus.
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Important Questions from Polynomials
Which of the following are zeros of the polynomial p(x) = x² - 5x + 6?
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x = 2, x = 3
Step 1: To find zeros, set p(x) = 0 Step 2: x² - 5x + 6 = 0 Step 3: Factor the quadratic: (x - 2)(x - 3) = 0 Step 4: Therefore x = 2 and x = 3 are the zeros Verification: p(2) = 4 - 10 + 6 = 0 ✓ and p(3) = 9 - 15 + 6 = 0 ✓
What is the degree of the polynomial 3x⁴ - 2x² + 7x - 5?
Which of the following expressions are polynomials?
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3x² + 2x - 1, 5x³ - x + 7
Step 1: A polynomial must have only non-negative integer exponents Step 2: 3x² + 2x - 1 has exponents 2, 1, 0 (all non-negative integers) ✓ Step 3: x⁻¹ + 2 has a negative exponent (-1) ✗ Step 4: 5x³ - x + 7 has exponents 3, 1, 0 (all non-negative integers) ✓ Step 5: √x + 3 = x^(1/2) + 3 has fractional exponent (1/2) ✗
The statement 'Every linear polynomial has exactly one zero' is:
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True
Step 1: A linear polynomial has the form ax + b where a ≠ 0 Step 2: To find its zero, set ax + b = 0 Step 3: Solving: ax = -b, so x = -b/a Step 4: Since a ≠ 0, there is exactly one solution Step 5: Therefore, every linear polynomial has exactly one zero
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