Question

Without solving, find the sum and product of zeroes:
$\frac{1}{3}{x}^2-5x+\frac{3}{2}$

Answer 1

Let $f\left(x\right)=\frac{1}{3}{x}^2-5x+\frac{3}{2}$

By comparing with $f\left(x\right)=a{x}^2+bx+c$

$a=\frac{1}{3},b=-5,c=\frac{3}{2}$

Sum of zeroes$(\alpha +\beta )=\frac{-b}{a}=\frac{-(-5)}{\left(\frac{1}{3}\right)}=5\times 3=15$

Product of zeroes$(\alpha .\beta )=\frac{c}{a}=\frac{\left(\frac{3}{2}\right)}{\left(\frac{1}{3}\right)}=\frac{3}{2}\times \frac{3}{1}=\frac{9}{2}$