Question

how to split a middle term with example and step by step explanation​

Answer 1

Step-by-step explanation:

Most of thequadratic equation problems which are asked can be easily split into their factors. If they can't be, only then do we go for the quadratic formula which gives the same answer but sometimes splitting the middle term gives us the answer much quicker.

In this method, the easiest pattern is the one where the term with degree 2 has unity as it's coefficient. All you have to do is look at the term with 'x' in it and the constant term.

We need to find 2 integers so that their sum is equal to the coefficient of term with power 1 and their product is equal to the constant.

For example:

$x^{2} - 5x + 6 = 0$

First split them into

$(x \: + \: )(x \: + \: )$

Now we need to fix the terms. So, what could be two integers which when added give -5 and when multiplied give +6? It could be 2 and 3, their signs ? Both negative since product is positive and sum is negative.

Therefore, the answer is...

$(x - 2)(x - 3) = 0$

Individually equate it to zero, we'll have

$x - 2 = 0 \\x = 2 \\ x - 3 = 0 \\ x = 3$

ie x has 2 roots, 2 and 3 (distinct and real is their nature)