Question

Check whether the following is a quadratic equation.
${x^2} - 2x = ( - 2)(3 - x)$

Answer 1

Hint: Try to solve and resemble the given equation with the quality of the quadratic equation.

Complete step-by-step answer:

On solving given equation, we’ll get,
\[
  {x^2} - 2x = ( - 2)(3 - x) \\
   \Rightarrow {x^2} - 2x = - 6 + 6x \\
   \Rightarrow {x^2} - 2x + 6 - 6x = 0 \\
   \Rightarrow {x^2} - 8x + 6 = 0 \\
 \]
This equation has the highest power of any term as 2. So, it’s a quadratic equation.

Note: We can also compare the solved equation with the standard form of the quadratic equation to get the result.