Solving Quadratic Equations by factoring

Example
solve x2+7x+12=0
The above equation is of the form ax2+bx+c=0 i.e. the general form of a quadratic equation.
what you need to do is find two numbers or factors, which we shall call T1 and T2. These two
terms are such that; i) their sum is b i.e. T1+T2=b , and ii) their product is ac i.e. T1×T
2=ac .
After gettoing the two terms, replace the term bx in the equation, with T1x and T2x ,to get
ax2+T1x +T2x+ c=0 . Then carry out group factorization i.e. you first factorize ax2+ T1x and
then +T2x+c.
So in our case, T1+T2=7 and T1×T
2=12. clearly our two terms are 3 and 4.
hence we replace 7x with 3x and 4x to get x2+3x+4x+12=0
then we apply group factorization to get x(x+3)+4(x+3)=0
note that (x+3) is a common factor.
so we have, (x+3)(x+4)=0
for the next step think of two numbers A and B and their product is zero i.e.AB=0. This imply
that either A or B is zero.
Hence in our case (x + 3)(x + 4) = 0, it implies either (x + 3) = 0 .(i) or (x + 4) =
0 (ii)
From (i) x=−3 and from (ii) x=−4
-3 and - 4 are called the roots of the equation x2+7x+12=0 or the solutins of the equation.
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