When will (m − 2)x² + 3x + 1 = 0 be quadratic?
Answer and explanation
Correct answer: m ≠ 2
The governing condition for a quadratic equation is that the coefficient of x² must be non-zero. Here that coefficient is m − 2. Therefore we require m − 2 ≠ 0. Solving this condition gives m ≠ 2. If m = 2, the x² coefficient becomes zero and the equation reduces to the linear equation 3x + 1 = 0, so it is no longer quadratic. The values m = 0 and m = 1 do keep the x² coefficient non-zero, but they are not the complete condition. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
m ≠ 2
Why is this the correct answer?
The governing condition for a quadratic equation is that the coefficient of x² must be non-zero. Here that coefficient is m − 2. Therefore we require m − 2 ≠ 0. Solving this condition gives m ≠ 2. If m = 2, the x² coefficient becomes zero and the equation reduces to the linear equation 3x + 1 = 0, so it is no longer quadratic. The values m = 0 and m = 1 do keep the x² coefficient non-zero, but they are not the complete condition. Thus option B is correct.
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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