What is the nature of the roots of 25x² − 30x + 9 = 0?
Answer and explanation
Correct answer: Equal real roots
For ax² + bx + c = 0, the discriminant D = b² − 4ac determines the nature of the roots. Here a = 25, b = −30, and c = 9, so D = (−30)² − 4(25)(9) = 900 − 900 = 0. A zero discriminant means the quadratic has two equal real roots. Indeed, the expression factors as 25x² − 30x + 9 = (5x − 3)², giving x = 3/5 twice. Therefore option A is correct. Distinct real roots require D > 0, no real roots require D < 0, and zero is not a root because the constant term is nonzero.
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What is the correct answer to this question?
Equal real roots
Why is this the correct answer?
For ax² + bx + c = 0, the discriminant D = b² − 4ac determines the nature of the roots. Here a = 25, b = −30, and c = 9, so D = (−30)² − 4(25)(9) = 900 − 900 = 0. A zero discriminant means the quadratic has two equal real roots. Indeed, the expression factors as 25x² − 30x + 9 = (5x − 3)², giving x = 3/5 twice. Therefore option A is correct. Distinct real roots require D > 0, no real roots require D < 0, and zero is not a root because the constant term is nonzero.
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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