What are the coefficients of the quadratic equation ax^2+ bx + c =0 if it has the roots -4 and 13/7?

The given quadratic equation is ax^2+bx+c
=0.

Given that this has roots -4 and
13/7.

We know that if x1 and x2 are the solutions of the
quadratic equeion ax^2+bx+c = o, then ax^2+nx+c = a(x-x1)(x-x2) is an
identiy.

So ax^2+bx+c = a(x-(-4))(x-13/7) is an
identity.

ax^2+bx+c = ax^2 -a(-4+13/7)x
-a*4*13/7

ax^2+bx+c = ax^2
+(15/7)ax-52a/7

Since the above is an identity, we can
equate like terms on both sides:

b = 15a/7 and c =
-52a/7.

Therefore for any a we choose  given b = 15a/y.  c
= -52a/7.  But cannot be zero. If a = 0, the equation degenerates into a linear
equation.