exam Maths Puzzle Numerical Ability

For the quadratic equation x^2 + kx +7 =0, if 3+sqrt2 is a root, what is the value of k ?
I said 6 but my teacher marked it wrong. Please help me :)

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exam Other Question
what are the three types of linear systems Hi! I need to reduce to lowest terms or rationalize.

(2(sqrt)3-1)(3(sqrt)3+4)

and

^3(sqrt)(-8x^12)

thanks in advance for the help