What is the nature of the roots of the equation 9x² + 12x + 4 = 0?
Answer and explanation
Correct answer: Two real and equal roots (D = 0)
Here, a = 9, b = 12, and c = 4. Therefore, the discriminant is D = b² − 4ac = 12² − 4 × 9 × 4 = 144 − 144 = 0. Hence, the roots are real and equal. In fact, 9x² + 12x + 4 = (3x + 2)², so the repeated root is x = −2/3. Option B would require D > 0, but the discriminant here is zero. Exam tip: For a quadratic equation, D = 0 indicates two equal real roots.
Frequently asked questions
What is the correct answer to this question?
Two real and equal roots (D = 0)
Why is this the correct answer?
Here, a = 9, b = 12, and c = 4. Therefore, the discriminant is D = b² − 4ac = 12² − 4 × 9 × 4 = 144 − 144 = 0. Hence, the roots are real and equal. In fact, 9x² + 12x + 4 = (3x + 2)², so the repeated root is x = −2/3. Option B would require D > 0, but the discriminant here is zero. Exam tip: For a quadratic equation, D = 0 indicates two equal real 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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