## RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1
- RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.2
- RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.3
- RD Sharma Class 10 Solutions Chapter 2 Polynomials VSAQS
- RD Sharma Class 10 Solutions Chapter 2 Polynomials MCQS

**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) = –

and product of zeroes (P) =

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 .

**Solution:**

**Question 4.**

If α and β are the zeros of the quadratic polynomial p(y) = 5y^{2} – 7y + 1, find the value of

**Solution:**

**Question 5.**

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

**Solution:**

**Question 6.**

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

**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

**Solution:**

**Question 12.**

If α and β are the zeros of the quadratic polynomial p(s) = 3s^{2} – 6s + 4, find the value of

**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 and

**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 and

**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)

**Solution:**

**Question 21.**

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

**Solution:**

Hope given RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.1 are helpful to complete your math homework.

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