form all the polynomial whose zeros are 7 + 2 root 2 and 7 minus 2 root 2
Answers
Answer:
k[x² - 14x + 41]
Step-by-step explanation:
Given roots are
(7 + 2√2) and (7 - 2√2)
⇒ Sum of zeroes = 7+2√2 + 7-2√2
= 7+7
= 14
⇒ Product of zeroes = (7+2√2)(7-2√2)
= 7(7-2√2) + 2√2(7-2√2)
= 49 - 14√2 + 14√2 - 4(2)
= 49 - 8
= 41
The quadratic polynomial is of the form
k[x² - (sum of zeroes)x + (product of zeroes)]
k[x² - 14x + 41]
where k is any constant.
You can put k = 1,2,3,.... , then we will get many (infinite) polynomials
⇒ k = 1,
the polynomial is x²-14x+41
⇒ k = 2,
the polynomial is 2[x² - 14x + 41]
2x² - 28x + 82
Like this, many polynomials can be found.
Hope this helps..!