SOLUTION: Find the value(s) of k that makes x^2 + (k+5)x + (5k+1) a perfect square trinomial.

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Question 987707: Find the value(s) of k that makes x^2 + (k+5)x + (5k+1) a perfect square trinomial.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+%28k%2B5%29x+%2B+%285k%2B1%29%22%22=%22%22%28x%2BA%29%5E2

x%5E2+%2B+%28k%2B5%29x+%2B+%285k%2B1%29%22%22=%22%22%28x%2BA%29%28x%2BA%29

x%5E2+%2B+%28k%2B5%29x+%2B+%285k%2B1%29%22%22=%22%22x%5E2%2B2Ax%2BA%5E2

Subtract x² from both sides:

%28k%2B5%29x+%2B+%285k%2B1%29%22%22=%22%222Ax%2BA%5E2

Equate the coefficients of x on each side

%28k%2B5%29%22%22=%22%222A

Equate the constant terms on each side:

5k%2B1%22%22=%22%22A%5E2

So we have this system of two equations in two unknowns:

system%28k%2B5=2A%2C5k%2B1=A%5E2%29

Solve the first equation for k

k = 2A-5

Substitute in the second:

5(2A-5)+1 = A²

10A - 25 + 1 = A²

0 = A² - 10A + 24

0 = (A - 6)(A - 4)

A - 6 = 0;  A - 4 = 0
    A = 6;      A = 4

k = 2A-5;     k = 2A-5
k = 2(6)-5;   k = 2(4)-5
k = 12-5;     k = 8-5
k = 3         k = 7

Edwin