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प्रश्न
Quadratic polynomials with rational coefficients having `sqrt(3)` as a zero are given by ______.
रिकाम्या जागा भरा
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उत्तर
Quadratic polynomials with rational coefficients having `sqrt(3)` as a zero are given by k(x2 – 3), where k is a constant.
Explanation:
If `sqrt(3)` is a root and coefficients are rational, its conjugate `-sqrt(3)` must also be a root, so the quadratic is `(x - sqrt(3))(x + sqrt(3)) = x^2 - 3`, up to multiplication by a rational constant.
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