# UP Board Solutions for Class 10 Maths Chapter 2 Exercise 2.2 Polynomials

## EXERCISE 2.2

### Sol. (i) We have,   x2 – 2x – 8  = x2 – 2x – 4x-8

= x(x + 2) – 4(x + 2)

= (x + 2)(x – 4)

The value of  x2 – 2x – 8  is zero when the value of (x + 2)(x – 4) is zero, i.e., when

x + 2 = 0 or x – 4 = 0, i.e.,

when x = – 2 or x = 4.

• The zeroes of x2 – 2x – 8    are – 2 and 4.

Therefore, sum of the zeroes = (-2) + 4 = 2

and,               product of zeroes = (- 2)(4) = – 8 =

### (ii) We have, 4s2 – 4s + 1 =-4s2 – 2s – 2s+1

= 2s(2s – 1) – 1(2s – 1)

= (2s – 1)(2s – 1)

The value of 4s2 – 4s + 1 is zero when the value of (2s – 1)(2s – 1) is zero, i.e.,

when 2s – 1 = 0 or 2s – 1 = 0,

i.e., when s = or s =

=The zeroes of 4s2 – 4s + 1 are   and

Therefore, sum of the zeroes =  + = 1

and,      product of zeroes

### (iii) We have,6x2 – 3 – 7x =6x2 – 7x – 3

= 6x2– 9x + 2x – 3

=3х(2x – 3) + 1(2x – 3)

=(3x + 1)(2x – 3)

The value of 6x2 – 3 – 7x  is zero when the value of

(3x + 1)(2x – 3) is zero, i.e., when 3x + 1 = 0 or 2x – 3 = 0,

i.e., when x = –  or x =

=> The zeroes of  6x2 – 3 – 7x  are –   and

Therefore, sum of the zeroes

and,        product of  zeroes

### (iv) We have, 4u2 +8u 4 = 4u(u + 2)

The value of 4u2 +8u   is zero when the value of 4u(u + 2) is zero, i.e., when u = 0

or   u + 2 = 0, i.e., when  u = 0 or u = – 2.

=> The zeroes of 4u2 +8u are 0 and – 2.

sum of the zeroes = 0 ÷ (-2) =- 2

### (vi) We have, 3x2 – x – 4   =3x2 -3 x – 4x- 4

= 3x(x + 1) – 4(x + 1)

= (x + 1)(3x – 4)

The value of 3x2 – x – 4  is zero when the value of (x + 1)(3x – 4) is zero, i.e.,

when x + 1 = 0 or 3x – 1 = 0, i.e.,

## 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Sol. (i) Let the polynomial be ax2 + bx + c, and its zeroes be a and . Then,

=> One quadratic polynomial which fits the given conditions is x2 – o.x +  , i.e., x 2 + .

### (iv) Let the polynomial be ax? + bx + c, and its zeroes be a and .

Then, a + = 1

a = 1

If a = 1, then b = -1and c = 1.

=> One quadratic polynomial which fits the given conditions is -x +1

### (v)Let the polynomial be ax2 + bx + c and its zeroes be a and .

Then,

If a = 4, then b = -1and c = 1.

=> One quadratic polynomial which fits the given conditions is 4x2 -x + 1.

### (vi) Let the polynomial be ax? + bx + c and its zeroes be a and B. Then,

If a = 4, then b = -4and c = 1.

=> One quadratic polynomial which fits the given conditions is x2 -4x + 1.