SOLUTION: Hello, I need help with the following math problem: "What is the product of all constants {{{ k }}} such that the quadratic {{{ x^2+kx+15 }}} can be factored in the form {{{

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello, I need help with the following math problem: "What is the product of all constants {{{ k }}} such that the quadratic {{{ x^2+kx+15 }}} can be factored in the form {{{       Log On


   

Question 1044084: Hello,
I need help with the following math problem:
"What is the product of all constants +k+ such that the quadratic +x%5E2%2Bkx%2B15+ can be factored in the form +%28x%2Ba%29%28x%2Bb%29+, where +a+ and +b+ are integers?"
Thank you,
Nicole
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The only factorizations of +x%5E2%2Bkx%2B15+ with integer coefficients are
(x+1)(x+15),
(x+3)(x+5),
(x-1)(x-15), and
(x-3)(x-5).

The coefficient of x in each case is 16, 8, -16, and -8, respectively, and their product is 16%2A8%2A-16%2A-8+=+16384.