If a quadratic equation has discriminant D = 49 − 16h², what are the values of h for equal roots?
Answer and explanation
Correct answer: h = 7/4 or h = −7/4
The governing rule is that a quadratic equation has equal roots exactly when its discriminant is zero. Hence we set the given expression equal to zero: 49 − 16h² = 0. Rearranging gives 16h² = 49, so h² = 49/16. Taking both square roots is essential because both positive and negative values have the same square. Therefore h = ±√(49/16) = ±7/4. Thus option A is correct. Substitution confirms it: for h = 7/4 or −7/4, 16h² = 49 and D = 0. Values ±7 would give D = 49 − 784, while ±4 would give D = 49 − 256; neither produces zero. The value h = 0 gives D = 49, which indicates distinct real roots, not equal roots.
Frequently asked questions
What is the correct answer to this question?
h = 7/4 or h = −7/4
Why is this the correct answer?
The governing rule is that a quadratic equation has equal roots exactly when its discriminant is zero. Hence we set the given expression equal to zero: 49 − 16h² = 0. Rearranging gives 16h² = 49, so h² = 49/16. Taking both square roots is essential because both positive and negative values have the same square. Therefore h = ±√(49/16) = ±7/4. Thus option A is correct. Substitution confirms it: for h = 7/4 or −7/4, 16h² = 49 and D = 0. Values ±7 would give D = 49 − 784, while ±4 would give D = 49 − 256; neither produces zero. The value h = 0 gives D = 49, which indicates distinct real roots, not 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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