# RD Sharma Solutions Class 10 Chapter 2 Polynomials Exercise 2.1

In this chapter, we provide RD Sharma Solutions for Class 10 Chapter 2 Polynomials Exercise 2.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 10 Chapter 2 Polynomials Exercise 2.1 pdf, free RD Sharma Solutions for Class 10 Chapter 2 Polynomials Exercise 2.1 book pdf download. Now you will get step by step solution to each question.

### RD Sharma Class 10 Solutions Polynomials Exercise 2.1

Question 1.
Find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their co-efficients : Solution:
(i) f(x) = x2 – 2x – 8                 Question 2.
For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization. Solution:
(i) Given that, sum of zeroes (S) = – (frac { 8 }{ 3 })
and product of zeroes (P) = (frac { 4 }{ 3 })   Question 3.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – 5x + 4, find the value of (frac { 1 }{ alpha } +frac { 1 }{ beta } -2alpha beta).
Solution: Question 4.
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 – 7y + 1, find the value of (frac { 1 }{ alpha } +frac { 1 }{ beta })
Solution:  Question 5.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – x – 4, find the value of (frac { 1 }{ alpha } +frac { 1 }{ beta } -alpha beta)
Solution: Question 6.
If α and β are the zeros of the quadratic polynomial f(x) = x2 + x – 2, find the value of (frac { 1 }{ alpha } -frac { 1 }{ beta })
Solution:  Question 7.
If one zero of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other, find the value of k.
Solution: Question 8.
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Solution: Question 9.
If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2.
Solution: Question 10.
If α and β are the zeros of the quadratic polynomial f(t) = t2 – 4t + 3, find the value of α4β3 + α3β4.
Solution: Question 11.
If α and β are the zeros of the quadratic polynomial f (x) = 6x4 + x – 2, find the value of (frac { alpha }{ beta } +frac { beta }{ alpha })
Solution:  Question 12.
If α and β are the zeros of the quadratic polynomial p(s) = 3s2 – 6s + 4, find the value of (frac { alpha }{ beta } +frac { beta }{ alpha } +2left( frac { 1 }{ alpha } +frac { 1 }{ beta } right) +3alpha beta)
Solution:  Question 13.
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p
Solution: Question 14.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – px + q, prove that: Solution:  Question 15.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – p(x + 1) – c, show that (α + 1) (β + 1) = 1 – c.
Solution: Question 16.
If α and β are the zeros of the quadratic polynomial such that α + β = 24 and α – β = 8, find a quadratic polynomial having α and β as its zeros.
Solution: Question 17.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – 1, find a quadratic polynomial whose zeros are (frac { 2alpha }{ beta }) and (frac { 2beta }{ alpha })
Solution:  Question 18.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – 3x – 2, find a quadratic polynomial whose zeros are (frac { 1 }{ 2alpha +beta }) and (frac { 1 }{ 2beta +alpha })
Solution:  Question 19.
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeros are (α + β)2 and (α – β)2.
Solution:  Question 20.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are :
(i) α + 2, β + 2
(ii) (frac { alpha -1 }{ alpha +1 } ,frac { beta -1 }{ beta +1 })
Solution:   Question 21.
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :  Solution:         All Chapter RD Sharma Solutions For Class10 Maths

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All Subject NCERT Exemplar Problems Solutions For Class10

All Subject NCERT Solutions For Class 10

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