RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10th

Q. No. 16 of Exercise 2A

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16

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is ‒1. Hence, find the zeros of the polynomial.

Let the zero of the polynomial be α and β

According to the question,


α + β = 0


αβ = -1


∴f(x)= x2 – (α + β)x + (αβ)


=x2 - 0x - 1


∴required polynomial f(x) = x2 - 1


Put f(x) = 0


x2 - 1 = 0


(x - 1)(x + 1)=0


x = 1 or x = -1


Chapter Exercises

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

More Exercise Questions

1

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 + 7x + 12
2

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 + 2x – 8
3

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 + 3x – 10
4

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

4x2 – 4x – 3
5

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

5x2 – 4 – 8x
6

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:
7

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

2x2 – 11x + 15
8

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

4x2 – 4x + 1
9

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x2 – 5
10

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

8x2 – 4
11

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

5y2 + 10y
12

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

3x2 – x – 4
13

Find the quadratic polynomial whose zeros are 2 and ‒6. Verify the relation between the coefficients and the zeros of the polynomial.
14

Find the quadratic polynomial whose zeros are . Verify the relation between the coefficients and the zeros of the polynomial.
15

Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial
16

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is ‒1. Hence, find the zeros of the polynomial.
17

Find the quadratic polynomial, the sum of whose zeros is and their product is 1. Hence, find the zeros of the polynomial.
18

Find the quadratic polynomial, the sum of whose roots is √2 and their product is 1/3.
19

If and x = ‒3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.
20

If (x + a) is a factor of the polynomial 2x2 + 2ax + 5x + 10, find the value of a.
21

One zero of the polynomial 3x3 + 16x2 + 15x – 18 is 2/3. Find the other zeros of the polynomial.

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