What is the nature of the roots of 9x² − 24x + 16 = 0?
Answer and explanation
Correct answer: Equal real roots
Use the discriminant D = b² − 4ac for the quadratic 9x² − 24x + 16 = 0. Here a = 9, b = −24, and c = 16, so D = (−24)² − 4(9)(16) = 576 − 576 = 0. Since the discriminant is zero, the equation has two equal real roots. The same result is visible from factorisation: 9x² − 24x + 16 = (3x − 4)². Thus both roots are x = 4/3, counted twice, and option A is correct. The other choices conflict with the zero-discriminant criterion.
Frequently asked questions
What is the correct answer to this question?
Equal real roots
Why is this the correct answer?
Use the discriminant D = b² − 4ac for the quadratic 9x² − 24x + 16 = 0. Here a = 9, b = −24, and c = 16, so D = (−24)² − 4(9)(16) = 576 − 576 = 0. Since the discriminant is zero, the equation has two equal real roots. The same result is visible from factorisation: 9x² − 24x + 16 = (3x − 4)². Thus both roots are x = 4/3, counted twice, and option A is correct. The other choices conflict with the zero-discriminant criterion.
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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