The factorization of a quadratic equation (mid - term splitting) leads to real roots of the equation. The quadratic equations when solved using the formula, it is the case where real and imaginary roots both are possible to occur. That is by using the direct formula also we are able to factorize the quadratic equation, but imaginary factors are possible. The direct formula for a quadratic equation wx2 + vx + z is given as follows: x = [- v ± Sq root(v2 – 4wz)] / 2w
The ±sign is put before the root sign because according to the property of root there are two possible roots when a root is solved. Thus we get either two real or two imaginary roots for our quadratic equation. In case of imaginary roots we can also say that the two roots are complex conjugate of each other. Let's us suppose an example of a quadratic equation to understand the factoring quadratic equations:
Suppose our quadratic equation is given as follows: 5x2 + 8x = -6. First we have to arrange the given equation such that it is present in the standard form of a quadratic equation and then start solving it. In our equation we can - not factorize by using mid - term splitting and so we need to use the direct formula to solve for x as follows:
Substituting the values of w, v and z in the formula we get,
x = [- 8 ± sq root(82 – 4 * 5 * (6))] / 2 * 5 ,
Thus we get x = -8/10 ±56i/10 .
According to the concept of Round to the Nearest Tenth, the values of the numbers are rounded to their nearest tenth number. For instance, 304 will be written as 300 and 256 is written as 260. These concepts are very important and have been explained in the icse sample papers 2013 in detail. (know more about How to factoring quadratic equations, here)
