If a quadratic has discriminant D = 25 - 4q², what are the values of q for equal roots?
Answer and explanation
Correct answer: q = 5/2 or q = -5/2
The governing concept is the discriminant criterion for a quadratic equation. If the discriminant D is zero, the two roots coincide and are therefore equal. Here D = 25 - 4q², so we set 25 - 4q² = 0. Rearranging gives 4q² = 25 and hence q² = 25/4. Taking both square roots is essential, because both a positive and a negative value have the same square: q = 5/2 or q = -5/2. Thus option A is correct. Option B would result from incorrectly using q² = 25, while options C and D do not make the discriminant zero.
Frequently asked questions
What is the correct answer to this question?
q = 5/2 or q = -5/2
Why is this the correct answer?
The governing concept is the discriminant criterion for a quadratic equation. If the discriminant D is zero, the two roots coincide and are therefore equal. Here D = 25 - 4q², so we set 25 - 4q² = 0. Rearranging gives 4q² = 25 and hence q² = 25/4. Taking both square roots is essential, because both a positive and a negative value have the same square: q = 5/2 or q = -5/2. Thus option A is correct. Option B would result from incorrectly using q² = 25, while options C and D do not make the discriminant zero.
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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