if the quadratic equation x^2+bx+c=0 has exactly 1 solution r, find b/c?

Answer 1

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is:

ax^2 + bx + c

where a ≠ 0. (For a = 0, the equation becomes a linear equation.)

In the above formula, the expression b^2 - 4ac is called the discriminant of the quadratic equation.

If the discriminant is positive, there are two distinct roots, both of which are real numbers. For quadratic equations with integer coefficients, if the discriminant is a perfect square, then the roots are rational numbers—in other cases they may be quadratic irrationals.

If the discriminant is zero, there is exactly one distinct root, and that root is a real number. Sometimes called a double root, its value is: -b/2a

If the discriminant is negative, there are no real roots. Rather, there are two distinct (non-real) complex roots, which are complex conjugates of each other.

http://en.wikipedia.org/wiki/Quadratic_equation is a good source for further details...

Answer 2

The first answer is correct; however, I think your final answer is to be given in terms of r (otherwise, why mention it?). If so, the quadratic formula gives (with b²-4c=0, as required for exactly one solution) r = -b/2 so

b = -2r and so

b/c = 4/b = 4/(-2r) = -2/r provided r≠0

(If r = 0, both b and c are 0 and the ratio b/c is undefined.)

Answer 3

You use the quadratic equation for this one
You know there is 1 solution so b^2-(4)(a)(c)=0
(Because if not there would be two answers becuase it is plus or minus radical b^2-(4)(a)(c))
so
b^2-(4)(c)(1)=0
b^2=4c
b=4c/b(divide by b)
b/c=4/b (divide by c)