Polynomials (NCERT Ch. 2)

• Understand the degree of a polynomial and classify linear, quadratic, and cubic polynomials.
• Find zeroes of a polynomial and relate them to its coefficients.
• Understand the relationship between zeroes and coefficients for quadratic polynomials.

1. A zero of a polynomial p(x) is a value of x for which p(x) = 0.
2. A linear polynomial (degree 1) has exactly 1 zero; a quadratic (degree 2) has at most 2 zeroes.
3. For a quadratic polynomial ax² + bx + c: sum of zeroes = -b/a, product of zeroes = c/a.
4. The graph of a quadratic polynomial is a parabola; the number of times it crosses the x-axis equals the number of real zeroes.

Find the zeroes of x² - 5x + 6 and verify the relationship with coefficients.

x² - 5x + 6 = (x-2)(x-3) = 0 -> x = 2 or x = 3
Sum of zeroes = 2+3 = 5 = -(-5)/1 = -b/a ✓
Product of zeroes = 2x3 = 6 = 6/1 = c/a ✓

• Forgetting the negative sign in the sum-of-zeroes formula (-b/a, not b/a).
• Confusing "zero of a polynomial" with "value of x-coefficient".
• Assuming every quadratic has 2 real zeroes (some have no real zeroes).

• Find the zeroes of x² - 7x + 12.
• If sum of zeroes = 5 and product = 6, form the quadratic polynomial.

Open the Practice tab for graded questions on Polynomials (NCERT Ch. 2).