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Problem:

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

Guest Dec 28, 2017

CPhill · Answer 1 · 2017-12-28T10:48:37

x^2 + 7x + 20 = 0

The sum of the roots = -7/1 = -7

The product of the roots is 20/1 = 20

So.....this implies that in Ax^2 + Bx + 1 = 0

-B/A = -7 ⇒ B/A = 7 ⇒ B = 7A

And

1/A = 20 ⇒ A = 1/20

So..... B = 7(1/20) = 7/20

So..... A + B = 1/20 + 7/20 = 8/20 = 2/5