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.

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 2 |

Chapter Name | Polynomials |

Exercise | 2.1 |

Category | RD Sharma Solutions |

**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) = x^{2} – 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 })

Required quadratic expression,

Question 3.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 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) = 5y^{2} – 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) = x^{2} – 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) = x^{2} + x – 2, find the value of (frac { 1 }{ alpha } -frac { 1 }{ beta })

Solution:

Question 7.

If one zero of the quadratic polynomial f(x) = 4x^{2} – 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) = kt^{2} + 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) = 4x^{2} – 5x – 1, find the value of α^{2}β + αβ^{2}.

Solution:

Question 10.

If α and β are the zeros of the quadratic polynomial f(t) = t^{2} – 4t + 3, find the value of α^{4}β^{3} + α^{3}β^{4}.

Solution:

Question 11.

If α and β are the zeros of the quadratic polynomial f (x) = 6x^{4} + 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) = 3s^{2} – 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) = x^{2} + 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) = x^{2} – px + q, prove that:

Solution:

Question 15.

If α and β are the zeros of the quadratic polynomial f(x) = x^{2} – 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) = x^{2} – 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) = x^{2} – 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) = x^{2} + 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) = x^{2} – 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) = ax^{2} + bx + c, then evaluate :

Solution:

**All Chapter RD Sharma Solutions For Class10 Maths**

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**All Subject NCERT Solutions For Class 10**

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