If p(x) = x² + 6x + 6, what is the correct classification of its zeroes?
Answer and explanation
Correct answer: Real and irrational
For p(x) = x² + 6x + 6, take a = 1, b = 6 and c = 6. The discriminant is D = b² − 4ac = 6² − 4(1)(6) = 36 − 24 = 12. Since D is positive, the two zeroes are real and distinct. Since 12 is not a perfect square, √12 is irrational, so the zeroes are irrational. The quadratic formula gives x = (−6 ± √12)/2 = −3 ± √3, confirming the result. Hence option A is correct. Option B would need a square discriminant, C would need a negative one, and D would need D = 0.
Frequently asked questions
What is the correct answer to this question?
Real and irrational
Why is this the correct answer?
For p(x) = x² + 6x + 6, take a = 1, b = 6 and c = 6. The discriminant is D = b² − 4ac = 6² − 4(1)(6) = 36 − 24 = 12. Since D is positive, the two zeroes are real and distinct. Since 12 is not a perfect square, √12 is irrational, so the zeroes are irrational. The quadratic formula gives x = (−6 ± √12)/2 = −3 ± √3, confirming the result. Hence option A is correct. Option B would need a square discriminant, C would need a negative one, and D would need D = 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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