RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10th

Q. No. 21 of Exercise 2C

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21

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

It is given in the question that,

Zeros of the polynomial x2 – 5x + k are


Also,


α- β = 1


Now by using the relationship between the zeros of the quadratic polynomial we have:


Sum of zeros = and product of zeros =


and


α + β=5 and α β = k/1


Now solving α- β=1 and α + β = 5, we get:


= 2


these values in we get:



Chapter Exercises

Exercise 2A
Exercise 2B
Exercise 2C
Multiple Choice Questions (MCQ)
Formative Assessment (Unit Test)

More Exercise Questions

1

If one zero of the polynomial x2 ‒ 4x + 1 is (2 + √3), write the other zero.
2

Find the zeros of the polynomial x2 + x ‒ p (p + 1).
3

Find the zeros of the polynomial x2 – 3x – m (m + 3).
4

Find α, β are the zeros of a polynomial such that α + β= 6 and αβ = 4 then write the polynomial.
5

If one zeros of the quadratic polynomial kx2 + 3x + k is 2 then find the value of k.
6

If 3 is a zero of the polynomial 2s2 + x + k, find the value of k.
7

If ‒4 is a zero of the polynomial x2 ‒ x (2k + 2) then find the value of k.
8

If 1 is a zero of the polynomial ax2 ‒ 3 (a ‒ 1) x ‒ 1 then find the value of a.
9

If ‒2 is a zero of the polynomial 3x2 + 4x + 2k then find the value of k.
10

Write the zeros of the polynomial x2 ‒ x ‒ 6.
11

If the sum of the zeros of the quadratic polynomial kx2 ‒ 3x + 5 is 1, write the value of k.
12

If the product of the zeros of the quadratic polynomial x2 ‒ 4x + k is 3 then write the value of k.
13

If (x + a) is a factor of (2x2 + 2ax + 5x + 10), find the value of a.
14

If (a ‒ b), a and (a + b) are zeros of the polynomial 2x3 ‒ 6x2 + 5x – 7, write the value of a.
15

If x3 + x2 ‒ ax + b is divisible by (x2 ‒ x), write the values of a and b.
16

If α and β are the zeros of the polynomial 2x2 + 7x + 5, write the value of α + β + αβ.
17

State division algorithm for polynomials.
18

The sum of the zeros and the product of zeros of a quadratic polynomial are -1/2 and ‒3 respectively. Write the polynomial.
19

Write the zeros of the quadratic polynomial f(X) = 6x2 ‒ 3.
20

Write the zeros of the quadratic polynomial f(x) = 4√3x2 + 5x ‒ 2√3.
21

If α and β are the zeros of the polynomial f(x) = x2 ‒ 5x + k such that α ‒ β = 1, find the value of k.
22

If α and β are the zeros of the polynomial f(x) = 6x2 + x ‒ 2, find the value of

23

If α and β are the zeros of the polynomial f(x) = 5x2 ‒ 7x + 1, find the value of

24

If α and β are the zeros of the polynomial f(x) = x2 + x – 2, find the value of

25

If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (A + b), find the a and b.

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