2.5 Quadratic Equations, SPM Paper 2 (Long Questions)


Question 9:
Solve the following quadratic equation:
4x (x + 4) = 9 + 16x

Solution:
4x( x+4 )=9+16x 4 x 2 +16x=9+16x    4 x 2 9=0 ( 2x ) 2 3 2 =0 ( 2x+3 )( 2x3 )=0 2x+3=0     or     2x3=0      2x=3                2x=3        x= 3 2                  x= 3 2    


Question 10:
Solve the following quadratic equation:
(x + 2)2 = 2x + 7

Solution:
( x+2 ) 2 =2x+7 x 2 +4x+4=2x+7 x 2 2x3=0 ( x+1 )( x3 )=0 x+1=0     or     x3=0      x=1                 x=3


Question 11:
Solve the following quadratic equation:
2 3x5 = x 3x1

Solution:
               2 3x5 = x 3x1          2( 3x1 )=x( 3x5 )               6x+2=3 x 2 5x 3 x 2 5x+6x2=0          3 x 2 +x2=0    ( 3x2 )( x+1 )=0 3x2=0     or     x+1=0      3x=2                  x=1        x= 2 3                  x=1


Question 12:
Solve the following quadratic equation:
5x+3 x 2 12x =6

Solution:
5x+3 x 2 12x =6 5x+3 x 2 =612x 3 x 2 +5x+12x6=0 3 x 2 +17x6=0 ( 3x1 )( x+6 )=0 3x1=0     or     x+6=0      3x=1                   x=6        x= 1 3                   x=6

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