Question

Reduce x²+7x+12/x²-6x-27

Answer 1

Given: x

2

+6x−7=0

x

2

+6x+9−9−7=0

x

2

+3x+3x+9=+16

x(x+3)+3(x+3)=16

(x+3)(x+3)=16

(x+3)

2

=±(4)

2

∴x+3=±4

2×a×b=6x

2×x×b=6x(∵a=x)

b=

2x

6x

b=3

b

2

=9

Taking square root on both the sides,

(Half of coefficient of x =

2

6

∴b=3)

If, x + 3 = 4 x +3 = - 4

x = 4 - 3 x = - 4 - 3

x = 1 x = - 7

∴ 1 and - 7 are the roots of x

2

+6x−7=0