What is the standard form of the equation \(4 = 3x - x^2\)?
Answer and explanation
Correct answer: x^2-3x+4=0
To write in standard form bring all terms to one side as \(ax^2+bx+c=0\). From \(4 = 3x - x^2\), moving the right-hand terms to the left changes signs: \(-x^2\) becomes \(+x^2\), \(+3x\) becomes \(-3x\), and \(+4\) stays. So the standard form is \(x^2-3x+4=0\). The closest distractor is option C (\(x^2-3x-4=0\)) which has the constant term sign wrong; option B has the sign of the linear term wrong. Exam tip: always rearrange to \(ax^2+bx+c=0\) and check sign changes when moving terms across ‘=’.
Frequently asked questions
What is the correct answer to this question?
x^2-3x+4=0
Why is this the correct answer?
To write in standard form bring all terms to one side as \(ax^2+bx+c=0\). From \(4 = 3x - x^2\), moving the right-hand terms to the left changes signs: \(-x^2\) becomes \(+x^2\), \(+3x\) becomes \(-3x\), and \(+4\) stays. So the standard form is \(x^2-3x+4=0\). The closest distractor is option C (\(x^2-3x-4=0\)) which has the constant term sign wrong; option B has the sign of the linear term wrong. Exam tip: always rearrange to \(ax^2+bx+c=0\) and check sign changes when moving terms across ‘=’.
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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