Weightage: 3 – 4 marks

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India’s Most Loved Science & Maths Videos – Packed in a Mobile App!

Introducing  Avanti Gurukul App

Avanti Gurukul App

Concepts covered:

  1. Zeroes of a polynomial
  2. Geometrical meaning of zeroes of a polynomial
  3. Relation between the zeroes and coefficients of a polynomial
  4. Division Algorithm for Polynomials

Expected questions:

  1. Questions based on finding zeroes of or using zeroes to find an unknown value are asked for 1 or 2 marks.
  2. Questions based on relation between the zeroes and coefficients of a polynomial or division algorithm for polynomials are asked for 3 or 4 marks.

Synopsis:

  1. Zeroes of a polynomial: A real number k is said to be a zero of the polynomial p(x) if p(k)=0, where, p(k)  is obtained by substituting k for x in the polynomial.
  1. Geometrical meaning of zeroes of a polynomial: The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y=p(x) intersects the x-axis.
  1. Relation between the zeroes and coefficients of a polynomial:
  • If α and β are the zeroes of a quadratic polynomial, ax2+bx+c then α+β= -b/a and αβ= c/a
  • If α, β and γ are the zeroes of a cubic polynomial, ax3+bx2+cx+d then α+β+γ= -b/a, αβ+βγ+γα= c/a and αβγ= -d/a
  1. Division algorithm for polynomials: The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that p(x)= g(x)q(x) + r(x), where r(x) = 0  or degree r(x) < degree g(x).

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