#Algebra Help :>
8 messages · Page 1 of 1 (latest)
Nice and clean
may i ask how you knew to divide and everything?
There is a faster solution.
For any equation $Ax^2 + Bx + C = 0$ with roots at $x=\alpha$ and $x=\beta$,
the sum of the roots / solutions is $\alpha + \beta = -\frac{B}{A}$.
Since you are given the sum $\alpha + \beta = k(4a + b)$, you can form an equation:
$\alpha + \beta = k(4a + b) = -\frac{-(16a + 4b)}{64}$
$\implies \quad k = \frac{4(4a + b)}{64(4a + b)} = \frac{1}{16}$