Equation whose roots are $3\pm \sqrt{2}$ is:
- $x^{2}+6x+2=0$
- $x^{2}-6x+7=0$
- $x^{2}+5x+7=0$
- $x^{2}-6x-7=0$
Reveal answer
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B
Correct answer
Explanation
For roots 3+sqrt(2) and 3-sqrt(2), the sum is 6 and the product is (3+sqrt(2))(3-sqrt(2)) = 9-2 = 7. The quadratic equation is x^2 - (sum)x + (product) = 0, which is x^2 - 6x + 7 = 0.
AI explanation
Given the roots of the equation are 3 plus the square root of 2 and 3 minus the square root of 2, we find the sum of the roots is 6. The product of the roots is 3 squared minus the square root of 2 squared, which is 9 minus 2, equaling 7. Using the standard form of a quadratic equation, x squared minus (sum of roots)x plus (product of roots) equals 0, we get x squared minus 6x plus 7 equals 0.