Multiple choice

If equation px2 + qx + r = 0 has one root as 2 - 3i, then what will be the values of p, q and r, respectively?

  1. 2, 12, 13

  2. 1, -4, 13

  3. 3, -2, 17

  4. 2, 4, 13

  5. None of these
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B Correct answer
Explanation

For a quadratic equation with real coefficients, complex roots occur in conjugate pairs. If 2 - 3i is a root, then 2 + 3i must also be a root. The quadratic is (x - (2 - 3i))(x - (2 + 3i)) = x^2 - 4x + 13 = 0, so p=1, q=-4, r=13.

AI explanation

Complex roots of a quadratic equation with real coefficients always occur in conjugate pairs, so the roots are 2 - 3i and 2 + 3i. Using the sum of roots formula, the sum is 4, making the coefficient of x equal to -4. Using the product of roots formula, the product is 22 + 32 = 13, which is the constant term. Assuming the leading coefficient p is 1, the values of p, q and r are respectively 1, -4 and 13.

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