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

Question

Mathematics

Nevaeh Calhoun

11 August, 18:40

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

+3

Answers (1)

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Faith Hoover · 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