Find the condition that the zeros of the polynomial may be in A.P.

RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10^th

Q. No. 4 of Exercise 2.2

Listen NCERT Audio Books - Kitabein Ab Bolengi

4

Find the condition that the zeros of the polynomial may be in A.P.

Let are the zeros of the given polynomial.

Sum of the zeros =

⇒ =

⇒ =

⇒ =

Since is the zero of the polynomial, therefore

=, we get

4

Chapter Exercises

Exercise 2.1

Exercise 2.2

Exercise 2.3

CCE - Formative Assessment

1

Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case:
(i)

(ii)

2

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, -1 and -3 respectively.

3

If the zeros of the polynomial are in A.P., find them.

4

Find the condition that the zeros of the polynomial may be in A.P.

5

If the zeros of the polynomial are in A.P., prove that .

6

If the zeros of the polynomial are in A.P., find the value of k.