Question

The quadratic x^2+7x+20$ has the same roots as the quadratic Ax^2+Bx+1 What is A+B?

Answer 1

If f(x)=x^2+7x+20 has the same roots as g(x)=Ax^2+Bx+1, then

one must be a multiple of the other.

By comparison of the constant terms, we know that 20g(x)=f(x), or

g(x)=(1/20)f(x)

=(1/20)(x^2+7x+20)

=(1/20)x^2 + (7/20)x + 20/20

=(1/20)x^2 + (7/20)x + 1

Therefore A=(1/20), B=(7/20),  and A+B=(1+7)/20=8/20=2/5