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The product of two of the roots of :x^4 - 11.x^3 + k.x^2 + 269.x - 2001 is 69. Find k.

The product of two of the roots of :x^4 - 11.x^3 + k.x^2 + 269.x - 2001 is 69. Find k. 

Grade:10

1 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-0.07}$ Let $x=a,b,c,d$ be the roots of equation. and given $ab=69$\\\\and $abcd=-2001$ So we get $cd=-29$.\\\\So $x^4-11x^3+kx^2+269x-2001=(x-a)(x-b)(x-c)(x-d)$\\\\So $x^4-11x^3+kx^2+269x-2001=(x^2+px+69)(x^2+qx-29)$\\\\ $x^4-11x^3+kx^2+269x-2001=+(p+q)x^3+(40+pq)x^2+(69q-29p)$\\\\So we get $p+q=-11,69q-29p=269\;,40+pq=k$\\\\

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