form an quadratic polynomial whose zeros are 2-√2/6 and 2+√2/6
Answers
Answer:
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 roots are
6
2−
2
,
6
2+
2
The sum and product of zeroes are
\text{sum of zeroes=}(\frac{2-\sqrt2}{6})+(\frac{2+\sqrt2}{6})sum of zeroes=(
6
2−
2
)+(
6
2+
2
)
=\frac{2-\sqrt2+2+\sqrt2}{6}=\frac{4}{6}=\frac{2}{3}=
6
2−
2
+2+
2
=
6
4
=
3
2
\text{Product of zeroes=}(\frac{2-\sqrt2}{6}).(\frac{2+\sqrt2}{6})Product of zeroes=(
6
2−
2
).(
6
2+
2
)
=\frac{1}{36}[(2-\sqrt2}{6})(2+\sqrt2}{6})
=\frac{1}{36}(4-2)=\frac{2}{36}=\frac{1}{18}=
36
1
(4−2)=
36
2
=
18
1
The quadratic polynomial is
x^2-(\text{sum of zeroes})x+(\text{product of zeroes})x
2
−(sum of zeroes)x+(product of zeroes)
x^2-\frac{2}{3}x+\frac{1}{18}x
2
−
3
2
x+
18
1
18x^2-12x+118x
2
−12x+1
which is required polynomial.