Multiple choice

Find the quadratic equation whose roots are $\displaystyle 3+\sqrt { 2 } ,3-\sqrt { 2 } $

  1. $\displaystyle { x }^{ 2 }+6x+5=0$
  2. $\displaystyle { x }^{ 2 }-6x-5=0$
  3. $\displaystyle { x }^{ 2 }-6x+7=0$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of roots = (3 + sqrt(2)) + (3 - sqrt(2)) = 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

The sum of the roots is (3 + sqrt(2)) + (3 - sqrt(2)) = 6, and the product is (3 + sqrt(2))(3 - sqrt(2)) = 9 - 2 = 7. Using the formula x^2 - (sum of roots)x + (product of roots) = 0, we substitute the values to get x^2 - 6x + 7 = 0.

Keep practicing — related questions