If \(p(x)=x^2-(3+\sqrt{2})x+3\sqrt{2}\), which is the correct pair of zeroes?
Answer and explanation
Correct answer: (3, \sqrt{2})
For a quadratic \(ax^2+bx+c\), the sum of roots is \(-b/a\) and the product is \(c/a\). Here \(a=1,\; b=-(3+\sqrt{2}),\; c=3\sqrt{2}\). So sum = \(3+\sqrt{2}\) and product = \(3\sqrt{2}\). These match the pair 3 and \(\sqrt{2}\), hence the zeros are 3 and \(\sqrt{2}\). The closest distractor \((3+\sqrt{2},0)\) is wrong because its product would be 0, not \(3\sqrt{2}\). Exam tip: verify roots quickly by checking sum and product or by factoring to \((x-3)(x-\sqrt{2})\).
Frequently asked questions
What is the correct answer to this question?
(3, \sqrt{2})
Why is this the correct answer?
For a quadratic \(ax^2+bx+c\), the sum of roots is \(-b/a\) and the product is \(c/a\). Here \(a=1,\; b=-(3+\sqrt{2}),\; c=3\sqrt{2}\). So sum = \(3+\sqrt{2}\) and product = \(3\sqrt{2}\). These match the pair 3 and \(\sqrt{2}\), hence the zeros are 3 and \(\sqrt{2}\). The closest distractor \((3+\sqrt{2},0)\) is wrong because its product would be 0, not \(3\sqrt{2}\). Exam tip: verify roots quickly by checking sum and product or by factoring to \((x-3)(x-\sqrt{2})\).
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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