EXERCISE 2.4

NCERT Solutions for Class 10 Maths Chapter 2 ( Polynomials)

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials of exercise 2.4 for all boards. We have updated all the contents for the new academic session 2020-2021.

In this chapter, you have studied the following points:

• Polynomials of degrees 1, 2, and 3 are called linear, quadratic, and cubic polynomials respectively.
• A quadratic polynomial in x with real coefficients is of the form ax²+ bx + c, where a, b, c are real numbers with a ≠ 0.
• 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.
• A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
• If α and β are the zeroes of the quadratic polynomial ax²+ bx + c, then α +β= −b/a ;       αβ= c/a
• If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d, then α + β + γ=−b/a;      αβ+ β γ + γ α=c/a ;      αβ γ=−b/a

• 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).