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NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4
Important Questions On Polynomials
1. Sum and product of two zeroes of x^4 – 4x³ – 8x² + 36x – 9 are 0 and – 9 respectively. Find the sum and product of its other two zeroes. [Answer: 4, 1]
2. Obtain zeroes of 4√3x²+5x – 2√3 and verify relation between its zeroes and coefficients. [Answer: -2/√3, √3/4]
3. What must be subtracted from 8x^4 + 14x³ – 2x² + 7x – 8 so that the resulting polynomial is exactly divisible by 4x² + 3x – 2? [Answer: 14x – 10]
4. Find all zeroes of the polynomial 2x³ + x² – 6x – 3 if two of its zeroes are 3 and – 3. [Answer: √3, -√3, – 1/2]
5. If √2 is a zero of (6x³ + √2x² –10x – 4√2), find its other zeroes. [Answer: -√2/2, -2√2/3]
Questions For Practice
1. On dividing the polynomial x³ – 5x² + 6x – 4 by a polynomial g(x), quotient and remainder are (x –3) and (– 3x + 5) respectively. Find g(x). [Answer: x² – 2x + 3]
2. What must be added to 4x^4 + 2x³ – 2x² + x – 1 so that the resulting polynomial is divisible by x² – 2x – 3? [Answer: 61x – 65]
3. If sum and product of two zeroes of the polynomial x³ + x² – 3x – 3 are 0 and 3 respectively, find all zeroes of the polynomial. [Answer: √3, -√3, -1]
4. If -1/2 is a zero of the polynomial 2x³ + x² – 6x – 3, find the sum and product of its other two zeroes. [Answer: 0, 3]
5. If α and β are zeroes of y² + 5y + m, find the value of m such that (α + β)² –αβ = 24. [Answer: 1]
Questions from Board Papers
1. Obtain all zeroes of the polynomial 2x^4 – 2x³ – 7x² + 3x + 6 if two factors of this polynomial are (x ± √3/2). [Answer: 2, -1, ±√3/2]
2. One zero of x³ – 12x² + 47x – 60 is 3 and the remaining two zeroes are the number of trees planted by two students. Find the total number of trees planted by both students. [Answer: 9]
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Image of the exercise 2.4
