# The coefficients a_2 and a_1 of a 2nd order polynomial a_2x^2+a_1x+a_0=0 are 3 and 5 respectively. One solution of the polynomial is 1/3. Determine the other solution?

Jan 19, 2017

## -2

#### Explanation:

${a}_{2} {x}^{2} + {a}_{1} x + {a}_{0} = 0$

${a}_{2} = 3$

${a}_{1} = 5$

one root is $\frac{1}{3}$

for a quadratic if $\alpha , \beta$ are the roots then

$\alpha + \beta = - {a}_{1} / {a}_{2}$

$\alpha \beta = {a}_{0} / {a}_{2}$

from the information given:

let $\alpha = \frac{1}{3}$

$\frac{1}{3} + \beta = - \frac{5}{3}$

$\beta = - \frac{5}{3} - \frac{1}{3} = - \frac{6}{3} = - 2$