Question

The solution of ${x^2} - 4x = 0$ is $x = 1,2$
A) True
B) False
C) Ambiguous
D) Data insufficient

Answer 1

Hint: The general quadratic equation is $a{x^2} + bx + c = 0$. Here \[c\] is zero. Now, we will factorize the equation by taking $x$ common from the equation. After that equate the factorization to 0. It will give the roots of the equation. Then check whether the roots given are the same as the roots derived from the equation.

Complete step by step solution:
The simple definition of a quadratic equation is the polynomial equation whose highest order is two. It commonly gets expressed as . In which, \[x\] is the unknown variable, and \[a,b,c\] are the constant terms. Also, note that ‘\[a\]’ is never equal to 0; otherwise, the equation becomes a linear one.
There are two fundamental concepts to solve a quadratic equation:
Formula method,
Factorization method.
These are the quickest methods to solve any quadratic equation.
Solving Quadratics by Factoring
Apart from the quadratic equation formula, factorization is another method of obtaining solutions for quadratic equations. Below are steps to find the solution of the quadratics by factoring.
You begin with an equation in the form of ax² + bx + c = 0.
Then, you factor the L.H.S. of the equation while assuming zero on the R.H.S. of the equation.
By assigning each factor to zero, you can solve the equation to obtain the values of x.
The given equation is ${x^2} - 4x = 0$.
Factorize the equation,
$ \Rightarrow x\left( {x - 4} \right) = 0$
Equate both equal to 0,
$x - 4 = 0$ and $x = 0$
Move 4 on the other side,
$\therefore x = 0, 4$
Since the roots of the equation are not equal to the given roots.

Hence, option (B) is correct.

Note: A quadratic equation is a polynomial equation of degree 2. A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
There are several methods you can use to solve a quadratic equation:
Factoring
Completing the Square
Quadratic Formula
Graphing
All methods start with setting the equation equal to zero.