# HOTs Polynomials 10 Mathematics

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 ax2 – 6x – 6 is 4, find the value of a.

-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?

2x2 + x – 6

Question. The value of quadratic polynomial f (x) = 2x2– 3x – 2 at x = -2 is ……

12

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

zeros = 3

Question. Find the zeroes of the polynomial x2 – 1.

+1

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

false

Question. Find the zeroes of the polynomial f(x) = 4√3x2 + 5x – 2√3

-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

f(x) = g(x)Xq(x) + r(x), deg r(x) = 0
x2 – 1 = (x+1)(x-1) + 0

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

–b/a

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

x2 – 1

Questions of 2 Mark

Question. If two zeroes of the polynomial of (x) = x4 – 6x3 – 26x2 + 138x – 35 are 2 ± √3 find other zeroes.

7, -5

Question. Obtain all the zeroes of the polynomial x2 + 7x + 10 and verify the relationship between the zeroes and its coefficients.

5, -2

Question. If α and β are the zeroes of the polynomial f(x) = x2 – px + q such that α2 + β2.

p2 – 2q

Question. If α and B are the zeroes of the quadratic polynomial f (x) = x2 + 2x + 1, then find 1/∞ and 1/β.

–2

Question. Check whether 2x3 + 1 is a factor of 2x5 + 10x4 + 6x3 + 2x2 + 5x + 1.

a = 1, b = + 2, Not a factor

Question. If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1,find the value of k.

k = 6

Question. If the polynomial f(x) = x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a

k = 5, a = -5

Question. Obtain all the zeroes of the polynomial f(x) = 3x4 + 6x3 – 2x– 10x – 5 if two of its zeroes are √5/3 and – √5/3

–1, -1

Question. Divide 3x2 – x3 – 3x + 5 by x – 1 – x2 and verify the division algorithm