Please refer to Polynomials HOTs Class 10 Mathematics provided below with Polynomials. All HOTs for Class 10 Mathematics with answers provided below have been designed as per the latest syllabus and examination petter issued by CBSE, NCERT, KVS. Students of Standard 10 Mathematics should learn the solved HOTS for Class 10 Mathematics provided below to gain better marks in examinations.

**Polynomials Class 10 Mathematics HOTs**

**Questions of 1 Mark**

**Question.** If the product of zeroes of the polynomial ax^{2} – 6x – 6 is 4, find the value of a.

## Answer

-3/2

**Question.****The sum and product of the zeroes of a quadratic polynomial are – 1/2 and –3 respectively. What is the quadratic polynomial?**

## Answer

2x^{2} + x – 6

**Question.** The value of quadratic polynomial f (x) = 2x^{2}– 3x – 2 at x = -2 is ……

## Answer

12

**Question.****Find the number of zeroes of y = p(x) from the graph**

## Answer

zeros = 3

**Question.****Find the zeroes of the polynomial x ^{2} – 1.**

## Answer

+1

**Question.****2x ^{2 }-3√x + 5 is a polynomial. True or false. Justify**

## Answer

false

**Question.****Find the zeroes of the polynomial f(x) = 4√3x ^{2} + 5x – 2√3**

## Answer

-2/√3,√3/4

**Question.****Give examples of polynomials f(x), g(x) and r(x) which justify the division algorithm f(x) = g(x) q(x)+r(x) and (i) deg r(x) = 0 (ii) deg f(x) =deg g(x) = 2 (iii) deg q(x) = deg r(x) = 1**

## Answer

f(x) = g(x)Xq(x) + r(x), deg r(x) = 0

x^{2} – 1 = (x+1)(x-1) + 0

**Question.****What is the zeroes of the polynomial ax + b = 0, a ≠ 0**

## Answer

–b/a

**Question.** Write a polynomial whose zeroes are √2 and -√2

## Answer

x^{2} – 1

**Questions of 2 Mark**

**Question.** If two zeroes of the polynomial of (x) = x^{4} – 6x^{3} – 26x^{2} + 138x – 35 are 2 ± √3 find other zeroes.

## Answer

7, -5

**Question.****Obtain all the zeroes of the polynomial x ^{2} + 7x + 10 and verify the relationship between the zeroes and its coefficients.**

## Answer

**–**5, -2

**Question.** If α and β are the zeroes of the polynomial f(x) = x^{2} – px + q such that α^{2} + β^{2}.

## Answer

p^{2} – 2q

**Question.****If α and B are the zeroes of the quadratic polynomial f (x) = x ^{2} + 2x + 1, then find 1/∞ and 1/β.**

## Answer

–2

**Question.** Check whether 2x^{3} + 1 is a factor of 2x^{5} + 10x^{4} + 6x^{3} + 2x^{2} + 5x + 1.

## Answer

a = 1, b = + 2, Not a factor

**Question.****If α and β are the zeroes of the polynomial f(x) = x ^{2} – 5x + k such that α – β = 1,find the value of k.**

## Answer

k = 6

**Question.****If the polynomial f(x) = x ^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by another polynomial x^{2} – 2x + k, the remainder comes out to be x + a, find k and a**

## Answer

k = 5, a = -5

**Question.** Obtain all the zeroes of the polynomial f(x) = 3x^{4} + 6x^{3} – 2x^{2 }– 10x – 5 if two of its zeroes are**√5/3 and – √5/3**

## Answer

–1, -1

**Question.** Divide 3x^{2} – x^{3} – 3x + 5 by x – 1 – x^{2} and verify the division algorithm

## Answer

Q – (x-2), R = 3

**Question.** Find the polynomial of least degree which should be subtracted from the polynomial x^{4} + 2x^{3} – 4x^{2} + 6 x -3 so that it is exactly divisible by x^{2} – x + 1

## Answer

2x – 2