Ncert Solutions for Class 10 Maths

Exercise 2.4 (Optional Exercise)

1. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case : (i) \(2x^3 + x^2 – 5x + 2\); \(1 \over 2\), 1, – 2 (ii) \(x^3 – 4x^2 + 5x – 2\); 2, 1, 1

2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

3. If the zeroes of the polynomial \(x^3 – 3x^2 + x + 1\) are a – b, a, a + b, find a and b.

4. If two zeroes of the polynomial \(x^4 – 6x^3 – 26x^2 + 138x – 35\) are \(2\pm \sqrt{3}\), find other zeroes.

5. If the polynomial \(x^4 – 6x^3 + 16x^2 – 25x + 10\) is divided by another polynomial \(x^2 – 2x + k\), the remainder comes out to be x + a, find k and a.

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