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The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?

 Jul 3, 2024
 #1
avatar+1267 
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We want two quadratics with the same constant and degree. So let's try converting the quadratic we are given. 

First, let's combine all like terms to the quadratic we are comparing to. We find that

\(2x^2 - 5x + 6 \)

 

Let's note the constant is different. Thus, we must divide this by 6 so that we have the same constant as Ax^2+Bx + 1. We have

\((1/3)x^2 - (5/6) x + 1\)

 

Thus, we know what A and B are. We simply plug those in and get

\(A + B = (1/3) - (5/6) = (2/6) - (5/6) = -3/6 = -1/2 \)

 

So -1/2 is our final answer. 

 

Thanks! :)

 Jul 3, 2024

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