There are two positive integers c for which the equation

5x^2+11x+c=4x^2 + 3x

has rational solutions. What is the product of those two values of c?

Guest Aug 22, 2021

#1**0 **

*There are two positive integers c for which the equation 5x^2+11x+c=4x^2 + 3x has rational solutions. What is the product of those two values of c?*

Start with 5x^{2} + 11x + c = 4x^{2} + 3x

Subtract (4x^{2} + 3x) from both sides x^{2} + 8x + c = 0

If c = 16, then the quadratic will factor to (x + 4)(x + 4)

If c = 15, then the quadratic will factor to (x + 5)(x + 3)

If c = 12, then the quadratic will factor to (x + 6)(x + 2)

If c = 7, then the quadratic will factor to (x + 7)(x + 1)

The problem says two. If that means ONLY two, then I'm misunderstanding the problem.

_{.}

Guest Aug 22, 2021