Question

Solve the given quadratic equation \[100{x^2} - 20x + 1 = 0\] by factorization?

Answer 1

Hint: The given question can be solved, by using factorization. Here we can factorize the given question by using the mid term splitting rule, in which we have to split the linear term and accordingly we can solve the question.
Formulae Used: Mid term splitting rule is used here,
For any equation \[{a^2} + ab + c\]
We have to split “b” in say “d” and “e” such that \[d \times e = ac\] and \[d + e = b\]for the above sample equation.
Now accordingly take the common factors about in a bracket and rest in another bracket and your answer will come i.e. factors will come from the taken equation.

Complete step-by-step answer:
Here the given question is \[100{x^2} - 20x + 1 = 0\], now using mid-term splitting rule, on solving we get:
\[
   \Rightarrow 100{x^2} - 20x + 1 = 0 \\
   \Rightarrow 100{x^2} - (10 + 10)x + 1 = 0 \\
   \Rightarrow 100{x^2} - 10x - 10x + 1 = 0 \\
   \Rightarrow 10x(10x - 1) - 1(10x - 1) = 0 \\
   \Rightarrow (10x - 1)(10x - 1) = 0 \]
Now the value of “x” will be:
\[ \Rightarrow 10x - 1 = 0 \\
   \Rightarrow x = \dfrac{1}{{10}} \\ \]
Here we got the answer for the given question.
Additional Information: You have to be careful while breaking the middle term and in calculating the product of the coefficient of first term and the last term, their respective signs have to be considered and accordingly signs between the split terms should be used.

Note: Midterm splitting is very easy technique to factories the equation, but in case it is not possible then you can adopt the maximum common factor technique in which you have to take common the maximum possible common factor from the equation and rest you can solve according to the same method used in the midterm common factor technique.