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Mudassar Nazar Notes Page 1

Exercise 1.1

Question No. 3

Part No. (vi)x2 2x 195 = 0

Solution

x2 2x 195 = 0x2 2x = 0 + 195x2 2x = 195x2 2x + (1)2 = 195 + (1)2( x 1 )2 = 195 + 1( x 1 )2 = 196

=x 1 = 14x 1 = 14 or x 1 = - 14x = 14 + 1 or x = -14 + 1x = 15 or x = -13S. S = { 15 , -13 }

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Mudassar Nazar Notes Page 2

Part No. (vii)-x2 + =

Solution-x

2- + = 0

-1(x2 + - ) = 0x2 + - = 0x2 + =x2 + + ( )2 = + ( )2

( x + )2 = +( x + )2 =( x + )2 =

=

x + = x + = or x + = -x = - or x = - -x = or x = -

x = or x = -5S.S = { , -5}

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Mudassar Nazar Notes Page 3

Part No. (viii)x2 + 17x + = 0

Solutionx

2+ 17x + = 0

x2 + 17x = 0 -x2 + 17x = - x2 + 17x + ( )2 =- + ( )2(x + )2 = - + (x + )2 =(x + )2 =

=x + =

x + = or x + = -x = - or x = -x = or x =x = or x =S.S = { , }

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Mudassar Nazar Notes Page 4

Part No. (ix)4 - =

Solution4 - =

=4 ( 3x + 1) 8 = 3x2 + 512x + 4 8 = 3x2 + 50 = 3x2 + 5 - 12x - 4 + 80 = 3x2 12x + 93x2 12x + 9 = 0

- + =x2 4x +3 = 0x2 4x + (2)2 = -3 + (2)2( x 2)2 = -3 + 4( x 2)2 = 1

=x 2 = 1x 2 = 1 or x -2 = -1x = 1 + 2 or x = -1 + 2x = 3 or x = 1S.S = { 3 , 1 }

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Part No. (x)7 ( x + 2a)2 + 3a2 = 5a ( 7x + 23a)

Solution7 [ (x)2 + 2(x)(2a) + (2a)2]+ 3a2 = 35ax + 115a27 [ x2 + 4ax + 4a2]+ 3a2 = 35ax + 115a27x2 + 28ax + 28a2 + 3a2 35ax 115a2 = 07x2 7ax 84a2 = 0

- - = 0x2 ax 12a2 = 0x2 ax = 0 + 12a2x2 ax = 12a2

x2 ax + = 12a2 +

( x - )2 =

=

x - =

x - = or x - = -

x = + or x = - +

x = or x =

x = or x =

x = 4a or x = -3a

S.S ={ 4a , -3a }

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Mudassar Nazar Notes Page 6

Exercise 1.2

Question No. 1

Part No. (vi)3x2 + 8x + 2 = 0

Solution3x2 + 8x + 2 = 0

Comparing it withax2 + bx + c = 0

a = 3 , b = 8 , c = 2By Quadratic formula

x =

x =

x =

x =

x =

x =

x =

x =

S.S = { }

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Mudassar Nazar Notes Page 7

Part No. (vii) = 1

Solution

= 1= 1

= 1

= 1-x + 9 = x2 11x + 300 = x2 11x + 30 + x 90 = x2 10x + 21x2 10x + 21 = 0

Comparing it withax2 + bx + c = 0

a = 1 , b = -10 , c = 21By Quadratic formula

x =

x =

x =

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Mudassar Nazar Notes Page 8

x =

x =

x = or x =

x = or x =x = 7 or x = 3S.S = { 7 , 3 }

Part No. (viii)

=Solution

==

=

=

=

=3( 3x2 x + 4) = 7 (2x2 2x)

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Mudassar Nazar Notes Page 9

9x2 3x + 12 = 14x2 14x0 = 14x2 14x - 9x2 + 3x - 120 = 5x2 11x -125x2 11x -12 = 0

Comparing it withax2 + bx + c = 0

a = 5 , b = -11 , c = -12By Quadratic formula

x =

x =

x =

x =

x =

x = or x =

x = or x =

x = 3 or x =

S.S = { 3 , }

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Mudassar Nazar Notes Page 10

Part No. (ix)+ = 2

Solution+ = 2

= 2

= 2

= 2ax a2 +bx b2 = 2(x2 bx ax + ab)ax a2 +bx b2 = 2x2 2bx 2ax + 2ab0 = 2x2 2bx 2ax + 2ab - ax + a2 -bx + b20 = 2x2 3ax 3bx + a2 + b2 + 2ab0 = 2x2 3(a + b)x + (a + b)22x2 3(a + b)x + (a + b)2 = 0

Comparing it withax2 + bx + c = 0

a = 2 , b = -3(a + b) , c = (a + b)2By Quadratic formula

x =

x =

x =

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Mudassar Nazar Notes Page 11

x =

x =

x = or x =

x = or x =

x = a + b or x =

S.S = { a + b , (a+b)}

Part No. (x)-(l + m) lx2 + (2l + m )x = 0 , l 0

Solution-lx2 + ( 2 l + m)x - (l + m) = 0-1[lx2 ( 2 l + m)x - (l + m)] = 0lx2 ( 2 l + m)x - (l + m) =lx2 ( 2 l + m)x - (l + m) = 0

Comparing it withax2 + bx + c = 0

a = l , b = -( 2 l + m) , c = l + mBy Quadratic formula

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Mudassar Nazar Notes Page 12

x =

x =

x =

x =

x =

x =

x =

x = or x =

x = or x =x = or x = 1

x= or x = 1

S.S = { , 1 }