Solve the following quadratic equation by factorization.
1(x−1)(x−2)+1(x−2)(x−3)+1(x−3)(x−4)=16
\(= (x-1)(x-4) = 18
= x^2-4x-x+4 =18
= x^2-5x-14=0
= x^2-7x+2x-14=0
= x(x-7)+2(x-7)=0
= (x-7)(x+2)=0 \)
Either x−7=0
Thereforex=7
Or,x+2=0
Therefore x=−2
The roots of the above mentioned quadratic equation are 7 and -2 respectively