If 5x² + 9x = 2, what is the equation in standard form?
Answer and explanation
Correct answer: 5x² + 9x − 2 = 0
A quadratic equation is commonly written in standard form as ax² + bx + c = 0, with a ≠ 0. Starting from 5x² + 9x = 2, subtract 2 from both sides to preserve equality: 5x² + 9x − 2 = 2 − 2 = 0. Thus the standard-form equation is 5x² + 9x − 2 = 0, which is option A. Option B results from changing the sign incorrectly while moving 2. Option C changes the sign of the 9x term without justification, and option D interchanges the coefficients of x² and x. No solving of the quadratic is required; the task only asks for rearrangement into standard form.
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What is the correct answer to this question?
5x² + 9x − 2 = 0
Why is this the correct answer?
A quadratic equation is commonly written in standard form as ax² + bx + c = 0, with a ≠ 0. Starting from 5x² + 9x = 2, subtract 2 from both sides to preserve equality: 5x² + 9x − 2 = 2 − 2 = 0. Thus the standard-form equation is 5x² + 9x − 2 = 0, which is option A. Option B results from changing the sign incorrectly while moving 2. Option C changes the sign of the 9x term without justification, and option D interchanges the coefficients of x² and x. No solving of the quadratic is required; the task only asks for rearrangement into standard form.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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