Question #2d2ff

Question

1249 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-19T18:39:36

$q = 6 and q = -6$

Let $r_1 =$ the first root
Let $r_2 =$ the second root
Given: $r_1-r_2=2$

$(x - r_1)(x - r_2) = x^2 - qx + 8$

$x^2 -r_2x -r_1x + r_1r_2 = x^2-qx+8$

$-r_1-r_2 = -q$
$r_1-r_2=2$
$r_1r_2=8$

Substitute for $r_2 = 8/r_1$ :

$-r_1-8/r_1 = -q$

$r_1-8/r_1=2$

$q = r_1+8/r_1" [1]"$

$r_1^2-2r_1-8=0" [2]"$

Factor equation [2]:

$(r_1-4)(r_1+2)$

$r_1 = 4 and r_1 = -2$

$q = 4 + 8/4 and q = -2+8/-2$

$q = 6 and q = -6$