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The equation of smallest degree with real co-efficients having 2 + 3i as one of the roots is : (a) x2 − 4x + 13 = 0 (b) x2 + 5x + 6 = 0 (c) x2 − 2x + 1 = 0 (d) x2 + 2x + 1 = 0 |
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Answer» Correct option (a) x2 − 4x + 13 = 0 Explanation: Since 2 + 3i is a root ∴ 2 − 3i is also a root Hence, required equation is x2 − (sum of roots) x + (product of roots) = 0 Sum of roots = 2 + 3i + 2 − 3i = 4 Product of roots = (2 + 3i) (2 − 3i) = 4 − 9i2 = 13 ∴ [ i2 = −1] So, equation is x2 − 4x + 13 = 0. |
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