Question

Derive a quadratic polynomial for which the sum of zeroes $=\frac{1}{3}$ and the product of zeroes $=\frac{1}{2}$ .

Answer 1

$x^2$-(Sum of roots)$x$ + (Product of roots)$=0$

Sum of roots$=\frac{1}{3}$

Product of roots$=\frac{1}{2}$

Hence the quadratic equation becomes $x^{2}-\dfrac{1}{3}x+\dfrac{1}{2}=0$

$x^2-\frac{2}{6}x+\frac{3}{6}=0$

$6x^2-2x+3=0$