Multiple choice

If one root of a quadratic equation is 3-√2, find the equation.

  1. x2+ 6x+5 = 0

  2. x2 - 9x + 7 = 0

  3. x2 - 6x + 7 = 0

  4. x2 + 6x - 7 = 0
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C Correct answer
Explanation

If one root is 3-sqrt(2), the other must be 3+sqrt(2). Sum of roots = 6. Product of roots = (3-sqrt(2))(3+sqrt(2)) = 9-2 = 7. The equation is x^2 - (sum)x + (product) = 0, which is x^2 - 6x + 7 = 0.

AI explanation

Since the coefficients of a quadratic equation are rational numbers, the irrational root 3 - √2 implies the existence of its conjugate root 3 + √2. The sum of these roots is (3 - √2) + (3 + √2) = 6, and their product is (3 - √2)(3 + √2) = 9 - 2 = 7. Using the standard form of a quadratic equation x^2 - (sum)x + (product) = 0, we substitute the values to get x^2 - 6x + 7 = 0.

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