Question

find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.2) √2 ,1/3​

Answer 1

by applying formula K(x^-x(sum of zeroes) +product of zeroes) ..here k is consonant

Answer 2

$\sqrt{2} , \frac{1}{3}$

Let the polynomial be

$ax²+bx+c$ and it's zeroes be

${\alpha}$ and $\beta .$

$\alpha + \beta = \sqrt{2} = \frac {3\sqrt{2}}{3} = \frac {-b}{a}$

${\alpha}{\beta} = \frac {1}{3} = \frac{c}{a}$

$\therefore a=3 , b=-3\sqrt{2} , c=1$

$\therefore$ Quadratic polynomial is $3x² - 3\sqrt{2x} +1$ .