RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 2. Polynomials

Subject: Maths - Class 10th

Q. No. 20 of Exercise 2.1

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20

If α and β are the zeros of the quadratic polynomial , then evaluate:

(i) (ii)


(iii) (iv)


(v) (vi)


(vii) (viii)

(i) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


⇒ On substituting values, we get


⇒ = =


(ii) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


⇒ On substituting values, we get


⇒ =


=


(iii) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


⇒ On substituting values, we get


⇒


(iv) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


⇒ On substituting values, we get


⇒=


(v) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


⇒= [Using (a + b)2 = a2 + b2 + 2ab]


On substituting values, we get


⇒=


⇒=


⇒=


(vi) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


= =


⇒ On substituting values, we get


=


⇒ =


(vii) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


=


⇒ = =


⇒ =


(viii) Let one root of the given quadratic polynomial is


Other root of the given quadratic polynomial is β



Sum of the roots = = =


Product of the roots = = =


=


⇒ + = =


On substituting values, we get


=


= = b


Chapter Exercises

Exercise 2.1
Exercise 2.2
Exercise 2.3
CCE - Formative Assessment

More Exercise Questions

1

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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

2

If α and β are the zeros of the quadratic polynomial, find the value of

3

If α and β are the zeros of the quadratic polynomial, find the value of .
4

If α and β are the zeros of the quadratic polynomial , find the value of

.
5

If α and β are the zeros of the quadratic polynomial , find the value of .
6

If α and β are the zeros of the quadratic polynomial , find the value of .
7

If α and β are the zeros of the quadratic polynomial , find the value of .
8

If α and β are the zeros of the quadratic polynomial , find the value of

.
9

If α and β are the zeros of the quadratic polynomial , find the value of .
10

If one zero of the quadratic polynomial is negative of the other, find the value of k.
11

If the sum of the zeros of the quadratic polynomial is equal to their product, find the value of k.
12

If the squared difference of the zeros of the quadratic polynomial is equal to 144, find the value of p.
13

If α and β are the zeros of the quadratic polynomial , prove that .
14

If α and β are the zeros of the quadratic polynomial , show that .
15

If α and β are the zeros of the quadratic polynomial such that and, find a quadratic polynomial having α and β as its zeros.
16

If α and β are the zeros of the quadratic polynomial , find a quadratic polynomial whose zeros are .
17

If α and β are the zeros of the quadratic polynomial , find a quadratic polynomial whose zeros are .
18

If α and β are the zeros of the quadratic polynomial , from a polynomial whose zeros are .
19

If α and β are the zeros of the quadratic polynomial , find a polynomial whose roots are (i) (ii) .
20

If α and β are the zeros of the quadratic polynomial , then evaluate:

(i) (ii)


(iii) (iv)


(v) (vi)


(vii) (viii)

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