Question

check whether 1/3 is a root of 3x^2+2x-1 or not

Answer 1

$f(x) = 3 {x}^{2} + 2x - 1 \\ f( \frac{1}{3}) = 3 \times {( \frac{1}{3} )}^{2} + 2 \times \frac{1}{3} - 1 \\ = 3 \times \frac{1}{9} + \frac{2}{3} - 1 \\ \frac{3}{9} + \frac{2}{3} - 1 \\ \frac{3 + 6 - 9}{9 } = \frac{0}{9} = 0 \\ hence \: \frac{1}{3} \: is \: root \: of \: f(x)$