Question

The roots of $x^2+8x+4$ are the same as the roots of $Ax^2+Bx+1$. What is $A+B$?
`The roots of $x^2+8x+4$ are the same as the roots of $Ax^2+Bx+1$. What is $A+B$?`

Answer 1

4.5

Explanation:

Hello, please consider the following.

First of all, let's assume that A is different from 0.

`x^2+8x+4\\\\\text{It means that the sum of the zeroes is -8 and the product is 4}\\\\Ax^2+Bx+1=A(x^2+(B)/(A)x+(1)/(A))\\\\\text{So the sum of the zeroes is } -(B)/(A) \text{ and the product is }(1)/(A)\\\\\text{It comes.}\\\\-(B)/(A)=-8 <=> (B)/(A)=8\\\\(1)/(A)=4`

So,

`A=(1)/(4)\\\\B=(8)/(4)=2\\\\A+B=(1+8)/(2)=(9)/(2)=4.5`

Thank you.