What is the standard form of \((x+2)(x-7)=3x\)?
Answer and explanation
Correct answer: \(x^2-8x-14=0\)
First expand the left side: \((x+2)(x-7)=x^2-7x+2x-14=x^2-5x-14\). To put in standard form \(ax^2+bx+c=0\), subtract \(3x\) from both sides: \(x^2-5x-14-3x=0\Rightarrow x^2-8x-14=0\). Option B (\(x^2-5x-14=0\)) is the expansion before moving \(3x\), so it is the closest distractor. Options C and D result from sign or arithmetic mistakes. Exam tip: Expand first, then bring all terms to one side and order by descending powers of \(x\).
Frequently asked questions
What is the correct answer to this question?
\(x^2-8x-14=0\)
Why is this the correct answer?
First expand the left side: \((x+2)(x-7)=x^2-7x+2x-14=x^2-5x-14\). To put in standard form \(ax^2+bx+c=0\), subtract \(3x\) from both sides: \(x^2-5x-14-3x=0\Rightarrow x^2-8x-14=0\). Option B (\(x^2-5x-14=0\)) is the expansion before moving \(3x\), so it is the closest distractor. Options C and D result from sign or arithmetic mistakes. Exam tip: Expand first, then bring all terms to one side and order by descending powers of \(x\).
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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