How will the roots of 3x² − 6x + 1 = 0 be?
Answer and explanation
Correct answer: Real, irrational and distinct
The discriminant of ax² + bx + c = 0 is D = b² − 4ac. In this equation, a = 3, b = −6 and c = 1. Thus D = (−6)² − 4(3)(1) = 36 − 12 = 24. A positive discriminant shows that the two roots are real and distinct. To decide whether they are rational or irrational, observe that 24 is not a perfect square. Indeed, the quadratic formula gives x = [6 ± √24]/6 = 1 ± √6/3, and √6 is irrational. Hence both roots are real, irrational and distinct. Therefore option A is correct. Option B would require a positive perfect-square discriminant, while options C and D correspond to D = 0 and D < 0 respectively.
Frequently asked questions
What is the correct answer to this question?
Real, irrational and distinct
Why is this the correct answer?
The discriminant of ax² + bx + c = 0 is D = b² − 4ac. In this equation, a = 3, b = −6 and c = 1. Thus D = (−6)² − 4(3)(1) = 36 − 12 = 24. A positive discriminant shows that the two roots are real and distinct. To decide whether they are rational or irrational, observe that 24 is not a perfect square. Indeed, the quadratic formula gives x = [6 ± √24]/6 = 1 ± √6/3, and √6 is irrational. Hence both roots are real, irrational and distinct. Therefore option A is correct. Option B would require a positive perfect-square discriminant, while options C and D correspond to D = 0 and D < 0 respectively.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
