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If (\sqrt{2}) and (\sqrt{3}) are zeroes of a quadratic polynomial, what type of coefficients will that polynomial have?
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Answer and explanation
Correct answer: At least one coefficient will be irrational
The sum (\sqrt{2}+\sqrt{3}) is irrational, so the coefficient of (x) in the monic polynomial is irrational. For rational coefficients, such zeroes must occur as conjugates.
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What is the correct answer to this question?
At least one coefficient will be irrational
Why is this the correct answer?
The sum (\sqrt{2}+\sqrt{3}) is irrational, so the coefficient of (x) in the monic polynomial is irrational. For rational coefficients, such zeroes must occur as conjugates.
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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