Question

find the quadratic polynomial whose zeroes are 2-root 2 ÷6 and 2+root 2 ÷6

find the quadratic polynomial whose zeros are 2 minus root 2 / 6 and 2 + root 2 / 6

Answer 1

Answer:

$\text{The quadratic polynomial is }18x^2-12x+1$

Step-by-step explanation:

Given the roots of the polynomial we have to find the quadratic polynomial

$\text{The roots are }\frac{2-\sqrt2}{6},\frac{2+\sqrt2}{6}$

The sum and product of zeroes are

$\text{sum of zeroes=}(\frac{2-\sqrt2}{6})+(\frac{2+\sqrt2}{6})$

$=\frac{2-\sqrt2+2+\sqrt2}{6}=\frac{4}{6}=\frac{2}{3}$

$\text{Product of zeroes=}(\frac{2-\sqrt2}{6}).(\frac{2+\sqrt2}{6})$

$=\frac{1}{36}[(2-\sqrt2}{6})(2+\sqrt2}{6})$

$=\frac{1}{36}(4-2)=\frac{2}{36}=\frac{1}{18}$

The quadratic polynomial is

$x^2-(\text{sum of zeroes})x+(\text{product of zeroes})$

$x^2-\frac{2}{3}x+\frac{1}{18}$

$18x^2-12x+1$

which is required polynomial.

Answer 2

Answer:

Hey

18x^2 - 12x + 1

hope this helps

pls mark my answer as brainliest

thank you