SOLUTION: Pls help in solving: if A and B are roots of the equation : {{{ 2x^2 + 5x + K=0}}} where K is constant and A - 2B=3 find the value of B and K

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Question 978196: Pls help in solving: if A and B are roots of the equation : +2x%5E2++%2B++5x+++%2B++K=0 where K is constant and A - 2B=3 find the value of B and K
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If +A+ and +B+ are the roots,
+%28+x+-+A+%29%2A%28+x+-+B+%29+=+2%2Ax%5E2+%2B+5x+%2B+K+
+2%2Ax%5E2+%2B+5x+%2B+K+=+0+
+x%5E2+%2B+%285%2F2%29%2Ax+%2B+K%2F2+=+0+
---------------------------
+x%5E2+-+A%2Ax+-+B%2Ax+%2B+A%2AB+=+x%5E2+%2B+%285%2F2%29%2Ax+%2B+K%2F2+
+x%5E2+%2B+%28+-A-+B+%29%2Ax+%2B+A%2AB+=+x%5E2+%2B+%285%2F2%29%2Ax+%2B+K%2F2+
---------------------
(1) +-A+-+B+=+5%2F2+
(2) +K%2F2+=+A%2AB+
(3) +A+-+2B+=+3+
-----------------
(1) +A+=+-B+-+5%2F2+
and
(3) +-B+-+5%2F2+-+2B+=+3+
(3) +-2B+-+5+-+4B+=+6+
(3) +6B+=+-5+-+6+
(3) +B+=+-11%2F6+
and
(3) +A+=+2B+%2B+3+
(3) +A+=+-11%2F3+%2B+9%2F3+
(3) +A+=+-2%2F3+
and
(2) +K%2F2+=+A%2AB+
(2) +K%2F2+=+%28-2%2F3%29%2A%28+-11%2F6+%29+
(2) +K%2F2+=+11%2F9+
(2) +K+=+22%2F9+
--------------------
+B+=+-11%2F6+
+K+=+22%2F9+
-----------------
check:
+%28+x+-+A+%29%2A%28+x+-+B+%29+=+2%2Ax%5E2+%2B+5x+%2B+K+
+%28+x+-+%28-2%2F3%29+%29%2A%28+x+-%28-11%2F6+%29+%29+=+2%2Ax%5E2+%2B+5x+%2B+22%2F9+
+x%5E2+%2B+%28+%282%2F3%29%2B%2811%2F6%29+%29%2Ax+%2B+22%2F18+=+2%2Ax%5E2+%2B+5x+%2B+22%2F9+
+x%5E2+%2B+%2815%2F6%29%2Ax+%2B+11%2F9+=+2%2Ax%5E2+%2B+%2830%2F6%29%2Ax+%2B+22%2F9+
+x%5E2+%2B+%2815%2F6%29%2Ax+%2B+11%2F9+=+0+
+2x%5E2+%2B+5x+%2B+22%2F9+=+0+
Hope I got it!