SOLUTION: Determine the value of 'k' if the product of the roots of 3kx^2+2(x-1)+k=0 is 1.

Question 119097: Determine the value of 'k' if the product of the roots of 3kx^2+2(x-1)+k=0 is 1.
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

The equation can also be expressed as

If i divide both sides of the given equation by , I get

matching up the terms, I get

The problem says the product of the roots = 1, so

solve for

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Step 1: Put the equation into standard form, i.e.

or more neatly:

Step 2: Apply the quadratic formula with , , and

Step 3: Simplify

Step 4: We are looking for k such that , so:

Step 5: This looks like a hideous mess to multiply, but remember that , so:

Step 6: Simplify and solve

So or

Step 7: can be excluded because that would make the lead coefficient on the original quadradic go to zero. Therefore,

Step 8: Check the answer. Using , the original quadratic becomes

The product of these two roots should be 1: Does ?

Again, we can simplify something that looks rather messy with the difference of two squares factorization, ,

: Answer checks.
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