In (q + 2)x² − 2(q − 1)x + q = 0, with q ≠ −2, what is the value of q for equal roots?
Answer and explanation
Correct answer: 1/4
Equal roots in a quadratic occur exactly when the discriminant is zero. Here a = q + 2, b = −2(q − 1), and c = q. Thus D = [−2(q − 1)]² − 4(q + 2)q = 4(q − 1)² − 4q(q + 2). Expanding gives D = 4(q² − 2q + 1 − q² − 2q) = 4(1 − 4q). Setting D = 0 gives 1 − 4q = 0, so q = 1/4. This value also satisfies q ≠ −2, so the equation remains quadratic. The other listed values make the discriminant nonzero and therefore do not produce equal roots.
Frequently asked questions
What is the correct answer to this question?
1/4
Why is this the correct answer?
Equal roots in a quadratic occur exactly when the discriminant is zero. Here a = q + 2, b = −2(q − 1), and c = q. Thus D = [−2(q − 1)]² − 4(q + 2)q = 4(q − 1)² − 4q(q + 2). Expanding gives D = 4(q² − 2q + 1 − q² − 2q) = 4(1 − 4q). Setting D = 0 gives 1 − 4q = 0, so q = 1/4. This value also satisfies q ≠ −2, so the equation remains quadratic. The other listed values make the discriminant nonzero and therefore do not produce equal roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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