What is the nature of the roots of 4x² − 12x + 9 = 0?
Answer and explanation
Correct answer: Equal real roots
The nature of roots can be determined by the discriminant D = b² − 4ac. For 4x² − 12x + 9 = 0, a = 4, b = −12, and c = 9. Thus D = (−12)² − 4(4)(9) = 144 − 144 = 0. A zero discriminant means the quadratic has two equal real roots. Indeed, the expression factors as 4x² − 12x + 9 = (2x − 3)², giving x = 3/2 twice. Therefore option A is correct; D > 0 would indicate distinct real roots and D < 0 would indicate no real roots.
Frequently asked questions
What is the correct answer to this question?
Equal real roots
Why is this the correct answer?
The nature of roots can be determined by the discriminant D = b² − 4ac. For 4x² − 12x + 9 = 0, a = 4, b = −12, and c = 9. Thus D = (−12)² − 4(4)(9) = 144 − 144 = 0. A zero discriminant means the quadratic has two equal real roots. Indeed, the expression factors as 4x² − 12x + 9 = (2x − 3)², giving x = 3/2 twice. Therefore option A is correct; D > 0 would indicate distinct real roots and D < 0 would indicate no real roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
