SOLUTION: Please help me solve this problem determine the value of k 3x^2 = 4x-k-1; one root is 1 more than 2x the other root

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please help me solve this problem determine the value of k 3x^2 = 4x-k-1; one root is 1 more than 2x the other root       Log On


   

Question 981898: Please help me solve this problem
determine the value of k
3x^2 = 4x-k-1; one root is 1 more than 2x the other root
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3x%5E2+-+4x+%2B+%28+k%2B1+%29+=+0+
using qudratic formula, the 2 roots make
the following equation from given data:


+%28+4+%2B+sqrt%28+16-12c+%29%29%2F6+=+2%2A%28+%28+4+-+sqrt%28+16-12c+%29%29%2F6+%29+%2B+1+
Multiply both sides by +6+
+4+%2B+sqrt%28+16+-+12c+%29+=+8+-+2%2Asqrt%28+16+-+12c+%29+%2B+6+
+3%2Asqrt%28+16+-+12c+%29+=+10+
+sqrt%28+16+-+12c+%29+=+10%2F3+
Squarte both sides
+16+-+2c+=+100%2F9+
+2c+=+144%2F9+-+100%2F9+
+2c+=+44%2F9+
+c+=+22%2F9+
and
+c+=+k+%2B+1+
+k+%2B+1+=+22%2F9+
+k+=+13%2F9+
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I'm not sure of the best way to check this:
I'll leave it up to you