CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 9

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10th CBSE

IMPORTANT

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If $α and β$ are zeroes of the polynomial $p (x) = 2 x^{2} + 5 x + k$ satisfying the relation $α^{2} + β^{2} + α β = \frac{21}{4}$ , then find the value of $k ?$

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Important Questions on Polynomials

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 10

If

α

and

β

are zeroes of the quadratic polynomial

k x^{2} + 4 x + 4

such that

α^{2} + β^{2} = 24

, then find the value of

k ?

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 10

If

α

and

β

are the zeroes of the polynomial

x^{2} - 5 x - k

such that

α - β = 1

, then find the value of

k ?

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 11

If one zero of the polynomial

x^{2} + 11 x + k

is

- 3

, find the value of

k

and other zero.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 12

Find the value of

k,

such that one zero of the polynomial

3 x^{2} + (1 + 4 k) x + k^{2} + 5

is one third of other.

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10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 13

If the zeroes of the polynomial

x^{2} + p x + q

are in the ratio

2 : 3

, then prove

6 p^{2} = 25 q .

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 14

If one zero of the polynomial

x^{2} - 8 x + k

exceeds the other by

2,

find the zeroes of the polynomial. Find the value of

k ?

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 15

If the sum and product of the zeroes of the polynomial

a x^{2} - 5 x + c

is equal to

10

each. Find the values of

a

and

c ?

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 2 - Polynomials>Exercise 2.3>Q 16

Find the quadratic polynomial whose sum and product of the zeroes are

- 1

and

- 20

respectively. Also, find the zeroes of the polynomial obtained.