Write \(2x(x+7)=0\) in standard form \(ax^2+bx+c=0\).
Answer and explanation
Correct answer: \(2x^2+14x=0\)
Core idea: use the distributive property. Multiply \(2x\) across the bracket: \(2x\cdot x=2x^2\) and \(2x\cdot7=14x\), giving \(2x^2+14x=0\). The closest distractor \(2x^2-14x=0\) is wrong because the sign of the linear term is incorrect. Option \(14x^2+2x=0\) swaps coefficients and is not equivalent; \(2x+7=0\) is linear, not quadratic. Exam tip: always expand and collect like terms to write the equation as \(ax^2+bx+c=0\) before choosing the answer.
Frequently asked questions
What is the correct answer to this question?
\(2x^2+14x=0\)
Why is this the correct answer?
Core idea: use the distributive property. Multiply \(2x\) across the bracket: \(2x\cdot x=2x^2\) and \(2x\cdot7=14x\), giving \(2x^2+14x=0\). The closest distractor \(2x^2-14x=0\) is wrong because the sign of the linear term is incorrect. Option \(14x^2+2x=0\) swaps coefficients and is not equivalent; \(2x+7=0\) is linear, not quadratic. Exam tip: always expand and collect like terms to write the equation as \(ax^2+bx+c=0\) before choosing the answer.
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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