SOLUTION: Dear Sir/Madam, A pleasant day! Please help me with this problem on quadratic equation: 3x^2-7x+6=k, roots equal to zero. Thank you very much for your help!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Dear Sir/Madam, A pleasant day! Please help me with this problem on quadratic equation: 3x^2-7x+6=k, roots equal to zero. Thank you very much for your help!      Log On


   

Question 767753: Dear Sir/Madam,
A pleasant day! Please help me with this problem on quadratic equation:
3x^2-7x+6=k, roots equal to zero. Thank you very much for your help!
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me with this problem on quadratic equation:
3x^2-7x+6=k, roots equal to zero.
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3x^2-7x+6=k
3x^2 = k + 7x - 6 = 0
k = -7x + 6

Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
"roots equal to zero", so you want the only root to be x=0.
(Look at "MORE DONE", below).

3x^2-7x+6-k=0
3x%5E2-7x%2B%286-k%29=0
-
x=0=%287%2B-sqrt%2849-4%2A3%2A%286-k%29%29%29%2F%282%2A3%29
We also need for discriminant to be equal to 0, otherwise we will have two roots and not both be zero.

49-4%2A3%286-k%29=0
49=12%286-k%29
49=72-12k
49-72=-12k
12k=72-49
k=23%2F12

Using that in the general solution gives that:
x=7%2F6-sqrt%2826%29%2F6 or x=7%2F6%2Bsqrt%2826%29%2F6
Neither of them is zero.
Your question or your equation does not work. What are you really asking?

MORE DONE:
Back to the quadratic formula solution equated to 0, you could find a k that makes the expression equal to zero for the roots to be equal to zero. You might be looking for that.
The numerator must then be zero.
0=7%2B-sqrt%2849-12%2A%286-k%29%29
49-12%286-k%29=49
-12%286-k%29=0
6-k=0
highlight%28k=6%29