## RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.3

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.3

**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.**

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in each of the following :

**Solution:**

**Question 2.**

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.

**Solution:**

**Question 3.**

Obtain all zeros of the polynomial f(x) = 2x^{4} + x^{3} – 14x^{2} – 19x – 6, if two of its zeros are -2 and -1.

**Solution:**

**Question 4.**

Obtain all zeros of f(x) = x^{3} + 13x^{2} + 32x + 20, if one of its zeros is -2.

**Solution:**

f(x) = x^{3} + 13x^{2} + 32x + 20

One zero = -2 or x = -2

x + 2 is a factor of f (x)

Now dividing f(x) by x + 2, we get

x + 1 = 0 => x = -1

and x + 10 = 0

=> x = -10

-1 and -10

Hence zeros are -10, -1, -2

**Question 5.**

Obtain all zeros of the polynomial f(x) = x^{4} – 3x^{3} – x^{2} + 9x – 6, if two of its zeros are – √3 and √3

**Solution:**

**Question 6.**

Find all zeros of the polynomial f(x) = 2x^{4} – 2x^{3} – 7x^{2} + 3x + 6, if its two zeros are and –

**Solution:**

**Question 7.**

Find all the zeros of the polynomial x^{4} + x^{3} – 34x^{2} -4x+ 120, if two of its zeros are 2 and -2.** [CBSE 2008]**

**Solution:**

Either x + 6 = 0, then x = -6

or x – 5 = 0, then x = 5

Hence other two zeros are -6, 5

and all zeros are 2, -2, -6, 5

**Question 8.**

Find all zeros of the polynomial 2x^{4} + 7x^{3} – 19x^{2} – 14x + 30, if two of its zeros are √2 and -√2

**Solution:**

**Question 9.**

Find all the zeros of the polynomial 2x^{3} + x^{2} – 6x – 3, if two of its zeros are – √3 and √3. **(CBSE 2009)**

**Solution:**

Let f(x) = 2x^{3} + x^{2} – 6x – 3

and two zeros of f(x) are – √3 and √3

**Question 10.**

Find all the zeros of the polynomial x^{3} + 3x^{2} – 2x – 6, if two of its zeros are – √2 and √2 **(CBSE2009)**

**Solution:**

**Question 11.**

What must be added to the polynomial f(x) = x^{4} + 2x^{3} – 2x^{2} + x – 1 so that the resulting polynomial is exactly divisible by x^{2} + 2x – 3 ?

**Solution:**

**Question 12.**

What must be subtracted from the polynomial f(x) = x^{4} + 2x^{3} – 13x^{2} – 12x + 21 so that the resulting polynomial is exactly divisible by x^{3} – 4x + 3 ?

**Solution:**

The resulting polynomial is exactly divisible by x^{2} – 4x + 3

Remainder = 0

=> 2x -3 – k = 0

=> k = 2x – 3

(2x – 3) must be subtracted

**Question 13.**

Given that √2 is a zero of the cubic polynomial 16x^{3} + √2x^{2} – 10x – 4√2 , find its other two zeroes.** [NCERT Exemplar]**

**Solution:**

**Question 14.**

Given that x – √5 is a factor of the cubic polynomial x^{3} – 3 √5 x^{2} + 13x – 3 √5 , find all the zeroes of the polynomial. **[NCERT Exemplar|**

**Solution:**

Hope given RD Sharma Class 10 Solutions Chapter 2 Polynomials Ex 2.3 are helpful to complete your math homework.

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