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प्रश्न
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
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उत्तर
Yes, consider the quadratic equation 2x2 + x – 4 = 0 with rational coefficient.
The roots of the given quadratic equation are `(-1 + sqrt(33))/4` and `(-1 - sqrt(33))/4` are irrational.
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Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
