SOLUTION: Please help me solve this problem : Find the value of the constant k such that the ratio of the two solution of the quadratic equation 2x2 - kx+ k +2 = 0 is 3:2

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Question 1075689: Please help me solve this problem : Find the value of the constant k such that the ratio of the two
solution of the quadratic equation 2x2 - kx+ k +2 = 0 is 3:2

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
No assumption of factorability for the given equation:
Roots using general solution formula,








Using the given ratio for the roots 3:2 the resulting ratio equation is
-

and algebraic steps lead to


Find discriminant,

General solution formula to get k







----------Mistake early in the steps makes all of the below wrong----------------
Work through the quadratic equation and find that .
Setup the next equation according to the ratio of the roots.

Simplify that and reach the equation .
If no mistakes were made in getting to this, then solve this quadratic equation for k. Discriminant is 1272.
General solution formula for quadratic equation results in
.

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
The solution by "josgarithmetic" is  TOTALLY  and  ABSOLUTELY   W R O N G .

Below find the correct solution.


Let "a" be one solution of the given equation   = .

Then the other solution is .


If so, then the given polynomial  admits factorization

 =  = (x-a)*(2x-3a) = .


It means that  -k = -5a, 3a^2 = k+2,   or  (substituting)

 = ,

 = 0  --->   =  = .


1.   =  = 1  ---->  k = 5a = 5;


2.   =  =  = .  ---->  k = 5a = .


Answer.  There are TWO solutions for k:  1) k = 5,   and   2)  k = .

Solved.


God save you of using the method that "josgarithmetic" uses.



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