If ((n² − 16)x² − 3x + 7 = 0) is a quadratic equation, what is the correct condition on n?
Answer and explanation
Correct answer: n ≠ ±4
A quadratic equation in x must have a non-zero coefficient of x². In the given equation, that coefficient is n² − 16. Therefore, the necessary condition is n² − 16 ≠ 0. Solving the equality that must be avoided gives n² = 16, so n = 4 or n = −4. Hence both values must be excluded, which can be written compactly as n ≠ ±4. Option A excludes only n = 4 and still permits −4, while option B excludes only −4 and still permits 4; both are incomplete. If option D were used, the x² coefficient would become zero and the equation would reduce to −3x + 7 = 0, which is linear. Thus option C is the only complete and correct answer.
Frequently asked questions
What is the correct answer to this question?
n ≠ ±4
Why is this the correct answer?
A quadratic equation in x must have a non-zero coefficient of x². In the given equation, that coefficient is n² − 16. Therefore, the necessary condition is n² − 16 ≠ 0. Solving the equality that must be avoided gives n² = 16, so n = 4 or n = −4. Hence both values must be excluded, which can be written compactly as n ≠ ±4. Option A excludes only n = 4 and still permits −4, while option B excludes only −4 and still permits 4; both are incomplete. If option D were used, the x² coefficient would become zero and the equation would reduce to −3x + 7 = 0, which is linear. Thus option C is the only complete and correct 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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