Question

Solve $ {x^2} - 2x = 0 $

Answer 1

Hint: The given problem requires us to solve an equation. The given equation can be reduced to a simple quadratic equation using a substitution. There are various methods that can be employed to solve a quadratic equation like completing the square method, using quadratic formulas and by splitting the middle term.

Complete step by step solution:
In the given question, we are required to solve the equation $ {x^2} - 2x = 0 $ .
Quadratic equations can be solved by various methods like splitting the middle term, using the quadratic formula, factoring the common factor, and completing the square method.
We can solve the given equation by any of the methods. But as the given equation is a simple one as each term consists of x. So, we can solve the equation through simple factorization.
Consider the equation $ {x^2} - 2x = 0 $ .
The equation can be factorized easily as x can be taken out common from both the terms in the equation.
So, $ {x^2} - 2x = 0 $
Taking x common from both the terms, we get,
\[ = x\left( {x - 2} \right) = 0\]
Now, either $ x = 0 $ or $ \left( {x - 2} \right) = 0 $ .
Either $ x = 0 $ or $ x = 2 $ .
So, the roots of the given equation $ {x^2} - 2x = 0 $ are: $ x = 0 $ and $ x = 2 $ .
So, the correct answer is “$ x = 0 $ and $ x = 2 $ ”.

Note: Quadratic equations are the polynomial equations with degree of the variable or unknown as $ 2 $ . Quadratic equations can be solved by splitting the middle term, factoring common factors, using the quadratic formula and completing the square method. The given equation can be solved by each and every method listed above.