Question

How do you solve \[{{x}^{2}}-4x=0\]?

Answer 1

Hint: To solve the type of question that has been mentioned above we will need to solve the quadratic equation but as there is no constant we can take x common from both the variables which will give us two values of x which will satisfy the equation.

Complete step-by-step answer:
In the above question we are provided with a quadratic equation which is \[{{x}^{2}}-4x=0\], in this equation we can see that there is no value of c so even if we don’t apply the quadratic formula to find the roots of equation we will be able to find the answer. To solve this question we just need to take x common which will then result us with
\[\Rightarrow x\left( x-4 \right)=0\]
Now in the above equation we can clearly see that there will be two cases for the answer in such a way that either \[x=0\]or \[\left( x-4 \right)=0\]this is the same as \[a\times b=0\] where a can be zero (0) or b can be zero (0). So now when we solve the two parts of the derived equation that has been stated as \[x=0\]and \[\left( x-4 \right)=0\] we will be able to find those two values of x which will satisfy the equation mentioned in the question. As the power of x in the equation mentioned in the question is 2 there will be only 2 roots for the equation which will satisfy the equation mentioned in the question. Now the two different derived equations are:
\[\Rightarrow x=0\]
\[\Rightarrow x-4=0\]
From the first one we can clearly see that the value of x will be equal to zero (0) so we have our first root as 0 now to find the second root of the equation we will check the second derived equation i.e. \[\left( x-4 \right)=0\]
\[\Rightarrow x=4\]
From this we will get the value of x as 4
Finally we have our two roots of the equation as x = 0 and 4.

Note: In the type of question that has been mentioned above we mainly forget that the root of equation where x is equal to zero (0) so always remember the power of x in the equation, higher the power more will be the number of roots so that you will not miss out on some of the roots of the equation which can be equal to zero (0).