# Finding polynomial from sum and product of zeroes

The question is

Form a quadratic polynomial whose sum of zeroes are $-1/3$ and product of zeroes are, $4$.

I did this,

$\alpha + \beta = \frac{-b}{a} = \frac{-1}{3}$

$\alpha \cdot \beta = \frac ca = 4$ Take $a=\operatorname{LCM}(4,1)$

$b = \frac{-1}{3}a = \frac{-4}{3} a$

$c= 4\times4 = 16$

So, $4x^2 - \frac{-4}{3}x + 16$

Is this correct ? I did it referring to another solution and don't get about the LCM part

LCM does not make sense here. The polynomial $$(x-\alpha)(x-\beta)$$ is zero precisely when $x=\alpha$ or $x=\beta$. Multiply this out and see if $\alpha+\beta$ or $\alpha\beta$ appear somewhere prominently (and can be replaced with $-\frac13$ and $4$).