Polynomials Grade 10

Choose correct answer(s) from the given choices

ID : kw -10-Polynom ials [1]

Grade 10 Polynomials

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(1)

If

one

zero

of

the

polynomial

2

(s

+

2

16)y

+

128y

+

8s

is

reciprocal

of

the

other,

what

is

the

value

of s ?

a. 5

b. 4

c. 3

d. 16

(2)

What

are

the

zeros

of

polynomial

p(x)

=

3

9x

+

2

46x

-

3x

-

40

?

9

a. -1, -5 and

8

b. -1, -5 and 8

8

c. -1, -5 and

9

d. None of these

11 (3) If a and b are the zeros of quadratic polynomial x2 + 3px - q, find the value of + .

a b

3p a.

q

-3p b.

q

6p c.

q

-6p d.

q

(4)

It

is

given

that

6

is

a

zero

of

the

polynomial

3

(x

+

2

2x

-

33x

-

90),

find

its

other

zeros.

a. -3 and - 5 c. 6

b. -1 and - 2 d. 3 and 5

(5) Find a quadratic polynomial whose zeros are reciprocals of the zeros of the polynomial . 2

x - x - 12

1

1

a.

2

k[x

-

x+

]

12

12

1

1

b.

2

k[x

+

x+

]

12

12

1

1

c.

2

k[x

-

x-

]

12

12

1

1

d.

2

k[x

+

x-

]

12

12

(6) Find the sum of the roots of the quadratic equation x2 - x - 20 = 0

a. 2

b. -1

c. 0

d. 1

Fill in the blanks

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ID : kw -10-Polynom ials [2]

(7)

The

real

number

should

be

subtracted

from

the

polynomial

-22

+

8x

+

2

84x

-

3

40x

so

that

(8x - 4) divides it exactly is

.

Answer the questions

(8)

Find

the

zeros

of

the

polynomial

f (x )

=

3

x

-

2

12x

+

47x

+

60,

if

it

is

given

that

product

of

its

two zeros is 15.

(9) Find the sum of the zeroes of the polynomial -m2 + m + 6.

1

1

(10)

If

and

are

the

zeros

of

quadratic

polynomial

2

x

+ x - 3, find the value of

+

.

3

3

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(1) b. 4

ID : kw -10-Polynom ials [3]

Grade 10 Polynomials

For more such worksheets visit

Step 1 Let one zero of the given polynomial be .

1

Then, the other zero is .

1

Product of zeros = ( ? ) = 1.

Step 2

constant term

8s

But, product of zeros =

=

.

coefficient of y2

(s2 + 16)

8s

2

= 1 (s + 16) = 8s

(s2 + 16)

2

s + 16 - 8s = 0

2

(s - 4) = 0

s-4= 0 s = 4

Step 3 Thus, the value of s is 4.

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8

(2) c. -1, -5 and

9

The

given

polynomial

is

p(x)

=

3

9x

+

2

46x

-

3x

-

40.

3

2

p(-1) = 9 ? (-1) + 46 ? (-1) - 3 ? -1 - 40

= 9 ? -1 + 46 ? 1 - 3 ? -1 - 40

= - 9 + 46 + 3 - 40

= 0

3

2

p(-5) = 9 ? (-5) + 46 ? (-5) - 3 ? -5 - 40

= 9 ? -125 + 46 ? 25 - 3 ? -5 - 40 = - 1125 + 1150 + 15 - 40 = 0

3

2

8

8

8

8

p( ) = 9 ? ( ) + 46 ? ( ) - 3 ?

- 40

9

9

9

9

512

2944

24

=

+

-

- 40

81

81

9

512 + 2944 - 216 - 3240

0

=

=

81

81

= 0

8

Thus, -1, -5 and are the zeros of the cubic polynomial p(x).

9

3p (3) a.

q

Step 1

3p

Since, sum of zeros = a + b = -

= -3p

1

Step 2

-q

Since, product of zeros = ab =

= -q

1

Step 3

1 1 a + b 3p

Therefore, + =

=

.

a b

ab

q

ID : kw -10-Polynom ials [4]

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(4) a. -3 and - 5

Step 1

Let 3

2

f(x) = x + 2x - 33x - 90.

Step 2 It is given that 6 is a zero of f(x), so (x - 6) is a factor of f(x).

Step 3 On, dividing f(x) by x - 6, we get:

x-6 )

3

2

2

x +2x -33x -90 ( x + 8x + 15

3

2

-(x -6x )

2

8x -33x -90

2

-(8x -48x)

15x -90 -(15x -90)

0

Step 4 Now,

3

2

f(x) = (x + 2x - 33x - 90)

2

= (x - 6)(x + 8x + 15)

2

= (x - 6)(x + 3x + 5x + 15)

= (x - 6)[x(x + 3) + 5(x + 3)]

= (x - 6)(x + 3)(x + 5)

Step 5 Therefore,

f(x) = 0 (x - 6)(x + 3)(x + 5) = 0 (x - 6) = 0 or (x + 3) = 0 or (x + 5) = 0 x = 6 or x = -3 or x = -5

Step 6 Thus, the other zeros are -3 and -5.

ID : kw -10-Polynom ials [5]

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