NCERT Solutions
Class 10 - Mathematics

Chapter 2: POLYNOMIALS

The graphs of \( y = p(x) \) are given in Fig. 2.10 for some polynomials \(p(x)\). Find the number of zeroes of \(p(x)\) in each case.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) \(x^2 - 2x - 8\)

(ii) \(4s^2 - 4s + 1\)

(iii) \(6x^2 - 3 - 7x\)

(iv) \(4u^2 + 8u\)

(v) \(t^2 - 15\)

(vi) \(3x^2 - x - 4\)

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) \(\dfrac{1}{4}, -1\)

(ii) \(\sqrt{2}, \dfrac{1}{3}\)

(iii) \(0, \sqrt{5}\)

(iv) \(1, 1\)

(v) \(-\dfrac{1}{4}, \dfrac{1}{4}\)

(vi) \(4, 1\)