If p(x) = 3x² − 12x + 6, what is the nature of its zeroes?
Answer and explanation
Correct answer: Two distinct irrational zeroes
For a quadratic ax² + bx + c, the discriminant D = b² − 4ac determines the nature of its zeroes. Here a = 3, b = −12 and c = 6, so D = (−12)² − 4(3)(6) = 144 − 72 = 72. This is positive, so the polynomial has two distinct real zeroes. Also, 72 is not a perfect square; therefore √D is irrational and the zeroes are irrational. Hence option C is correct. Option A would require D = 0, option B would require a positive perfect-square discriminant, and option D would require D < 0.
Frequently asked questions
What is the correct answer to this question?
Two distinct irrational zeroes
Why is this the correct answer?
For a quadratic ax² + bx + c, the discriminant D = b² − 4ac determines the nature of its zeroes. Here a = 3, b = −12 and c = 6, so D = (−12)² − 4(3)(6) = 144 − 72 = 72. This is positive, so the polynomial has two distinct real zeroes. Also, 72 is not a perfect square; therefore √D is irrational and the zeroes are irrational. Hence option C is correct. Option A would require D = 0, option B would require a positive perfect-square discriminant, and option D would require 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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