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SMO 2009 Junior Round 1 Question 27

SMO · SMO 2009 Junior Round 1

Question 27

Let $x_1,x_2,x_3,x_4$ denote the four roots of the equation
$$x^4+kx^2+90x-2009=0.$$
If $x_1x_2=49$, find the value of $k$.