Which option shows the common mistake when converting the equation \(x^2 = 5x - 6\) to standard form?
Answer and explanation
Correct answer: \(x^2 - 5x - 6 = 0\)
The correct standard form is \(x^2 - 5x + 6 = 0\). To convert, bring all terms to one side and set the equation equal to zero; moving \(-6\) from the right to the left changes its sign to \(+6\). Option (B) shows the common mistake where the sign of \(-6\) was not changed, so it is the wrong conversion and therefore the required 'common mistake'. The closest distractor (D) simply leaves the equation unchanged and is not in standard form; (C) unnecessarily writes \(0x\), which is not the standard conversion. Exam tip: always move all terms to one side, flip signs when moving terms, combine like terms and set equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(x^2 - 5x - 6 = 0\)
Why is this the correct answer?
The correct standard form is \(x^2 - 5x + 6 = 0\). To convert, bring all terms to one side and set the equation equal to zero; moving \(-6\) from the right to the left changes its sign to \(+6\). Option (B) shows the common mistake where the sign of \(-6\) was not changed, so it is the wrong conversion and therefore the required 'common mistake'. The closest distractor (D) simply leaves the equation unchanged and is not in standard form; (C) unnecessarily writes \(0x\), which is not the standard conversion. Exam tip: always move all terms to one side, flip signs when moving terms, combine like terms and set equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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