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CHAPTER 2 - POLYNOMIALS
MULTIPLE CHOICE QUESTIONS
- The zeroes of
x
2
− 2 x − 8
are:
(a) (2, −¿
(b) (4, −¿
(c) ( −¿
- (d) ( −¿
- The quadratic polynomial whose sum and the product of zeroes √ 2 ,
respectively is:
(a)
3 x
2
√
2 x + 1
(b)
3 x
2
√
2 x + 1
(c)
3 x
2
√
2 x − 1
(d)
− 3 x
2
√
2 x + 1
- If the zeroes of the quadratic polynomial
a x
2
+ bx + c , c ≠ 0
are equal, then
(a) c and b have opposite signs (b) c and a have opposite signs
(c) c and b have same signs (d) c and a have same signs
- Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number
of points where the graph of polynomial is:
(a) Intersects x-axis (b) Intersects y-axis
(c) Intersects y-axis or x-axis (d) Doesn’t meet any axis
- A polynomial of degree n has:
(a) Only one zero (b) At least n zeroes
(c) More than n zeroes (d) At most n zeroes
- The number of polynomials having zeroes as -2 and 5 is:
(a) 1 (b) 2 (c) 3 (d) More than 3
- Zeroes of
p ( x )= x
2
are:
(a)
√
(b)
√
(c)
√
(d)
√
- If one zero of the quadratic polynomial
x
2
+ 3 x + k
is 2, then the value of k is:
(a) 10 (b) –10 (c) 5 (d) –
- A quadratic polynomial, whose zeroes are –3 and 4, is:
(a)
x
2
− x + 12
(b)
x
2
(c)
x
2
x
(d)
2 x
2
+ 2 x − 24
- The zeroes of the quadratic polynomial
x
2
+ 99 x + 127
are:
(a) both positive (b) both negative
(c) one positive and one negative (d) both equal
- The zeroes of the quadratic polynomial
x
2
+ 7 x + 10
are:
(a) −¿
3 (b) 2, 5 (c) −¿
5 (d) −¿
- If the graph of a polynomial intersects the x-axis at three points, then number of zeroes are:
(a) Three (b) Two (c) Four (d) More than three
ASSERTION – REASON BASED QUESTION
In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the
correct answer out of the following choices :
(a) Both assertion ( A ) and reason ( R ) are true and reason ( R ) is the correct explanation of assertion ( A ).
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
(c) Assertion ( A ) is true but reason ( R ) is false.
(d) Assertion ( A ) is false but reason ( R ) is true.
13.Assertion:If ( 2 − √
) is one zero of quadratic polynomial then the other zero is (
2 + √
Reason: Irrational zeroes (roots) occur in pairs
14.Assertion:If one zero of the polynomial p ( x )=( k
2
2
+ 13 x + 4 k
is reciprocal of the other, then
k = 2
Reason: If
( x − a )
is a factor of
p ( x )
, then
p ( a )= 0
, i.e a is a zero of
p ( x )
15.Assertion:
x
2
+ 7 x + 12
has no real zeroes
Reason: A quadratic polynomial can have at most two real zeroes.
ANSWERS
1 (b) (4,−¿2) 2(a)
3 x
2
√
2 x + 1
3(d) c and a have same signs 4(a) Intersects x-axis
5(d) At most n zeroes 6 (d) More than 3 7(b)
√
8(b) −¿
9(c)
x
2
x
10(b) both negative 11 (c) −¿
5 12(a) Three
13(a) 14 (c) 15 (d)
CASE STUDY 3:
A ball is thrown in air so that t seconds after it is thrown, its height h metre above its
starting point is given by the polynomial
h = 25 t − 5 t
2
Observe the graph of the polynomial and answer the following questions:
(a)Write zeroes of the given polynomial.
(b)Find the maximum height achieved by ball.
(c)After throwing upward, how much time did the ball take to reach the height of 30 m?
OR
Find the two different values of t when the height of the ball was 20 m.
ANSWERS
CASE STUDY 1: (a) Parabola (b) a > 0 (c) Quadratic Polynomial OR a ≠ 0
CASE STUDY 2: (a) 3 (b) –3, –1, 2 (c) x
3
2
CASE STUDY 3: (a) 0 and 5 (b) 31.25 units (c) 2 or 3 OR 4 or
SUBJECTIVE QUESTIONS
1.If
are the zeroes of the polynomials
x
2
− px + q
then find the value of the following:
(i) α
2
2
( ii ) α
3
3
( iii )
(iv) α − β (v)
3
3
2.Find the zeroes of the polynomial:
(i)
x
2
+ 2 x + 1
(ii)
x
2
− x − 6
3.Find the zeroes of each of the following polynomials and verify the relationship between its zeroes and
coefficients.
(i)
3 x
2
− x − 4 ( ii ) 4 x
2
√
2 x − 3 ( iii ) 9 x
2
− 4 ( iv ) x
2
+ 5 x + 6
(v)
6 x
2
− 3 − 7 x
(vi)
5 x
2
− 4 − 8 x
(vii)
2 x
2
− 9 − 3 x
(viii)
x
2
− 5 x − 6
- Find the quadratic polynomial, the sum and product of whose zeroes are respectively.
(i) 5 and 6 (ii) √
and
(iii) 2 and – 3 (iv)
and
5.Find the quadratic polynomial whose zeroes are: -
(i) 2 and – 2 (ii) 3 and – 2 (iii) 3 + √
and 3 − √
(iv)
p + 2 q
and
p − 2 q
(v) – 5 and 4
- Find the value of k if the quadratic polynomial
2 x
2
− 3 kx + 5
has 9 as the sum of its zeroes.
- If the sum of zeroes of the polynomial
f ( x )= px
2
− 4 x + 2 p
is same as their product, find the value of p.
8.What would be the relation between p and q if zeroes of quadratic polynomial
px
2
+ 2 x + q
are reciprocal
of each other.
- Find the condition on the coefficients of quadratic polynomial
a x
2
+ bx + c
, so that zeroes of this
polynomial are equal in magnitude opposite in sign.
10. If α , β are the zeroes of quadratic polynomial
x
2
− p ( x + 2 )− c
, then prove that
( α + 2 ) ( β + 2 )− 4 + c = 0.
11.Let
be the zeroes of quadratic polynomial
2 x
2
+ 3 x + 1
. Obtain a quadratic polynomial whose
zeroes are: -
(i)
and
(ii)
,
12.If α, β are the zeroes of quadratic polynomial 2x² + 5x + k, find the value of k such that (α + β)² - αβ =24.
- How many zeros does the polynomial
( x − 3 )
2
have? Also, find its zeroes.
14.α and β are zeroes of the quadratic polynomial x
2
- 6x + y. Find the value of ‘y’ if 3α + 2β = 20.
- Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial
f(x) = ax
2
25 x
2
− 30 x + 4
x
2
− 15 x + 54
