emily4984
03.12.2021 •
Mathematics
Q.If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is
Solved
Show answers
More tips
- C Computers and Internet What is Web 2.0 and How Does it Work?...
- S Style and Beauty Is Photoepilation the Solution to Unwanted Hair Forever?...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
- F Food and Cooking How to Get Reconfirmation of Registration?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
- F Family and Home How to Get Rid of Your Neighbors?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
Answers on questions: Mathematics
- M Mathematics Anyone know this?????...
- M Mathematics Given: Quadrilateral ABCD is a parallelogram, Prove: BAD DCB. and ABC CDA. Match each Statement to its corresponding rea......
- M Mathematics Lim (x— 1)x^2 +3x-4/x-1...
- W World Languages Project Exam Lesson Name: DEVELOPING IDEAS Exam number: 700138 written exam....
- M Mathematics Who wanna ta lk im bore d...
- M Mathematics 2x - 3 x² + 5x – 4 which expression represents the area of the rectangle shown below...
- S Spanish Which sentence correctly describes the picture? El museo tiene objetos de gran valor cultural. B Las ruinas son muy antiguas. El templo es muy hermoso D. La laguna es muy...
Ответ:
(a) Let p(x) = x3 + ax2 + bx + c
Let a, p and y be the zeroes of the given cubic polynomial p(x).
∴ α = -1 [given]
and p(−1) = 0
⇒ (-1)3 + a(-1)2 + b(-1) + c = 0
⇒ -1 + a- b + c = 0
⇒ c = 1 -a + b …(i)
We know that,
--------------
refer to attatchment#1
--------------
αβγ = -c
⇒ (-1)βγ = −c [∴α = -1]
⇒ βγ = c
⇒ βγ = 1 -a + b [from Eq. (i)]
Hence, product of the other two roots is 1 -a + b.
Alternate Method
Since, -1 is one of the zeroes of the cubic polynomial f(x) = x2 + ax2 + bx + c i.e., (x + 1) is a factor of f{x).
Now, using division algorithm,
-------------------------------
refer to attatchment #2
----------------------------------
⇒x3 + ax2 + bx +c = (x + 1) x {x2 + (a – 1)x + (b – a + 1)> + (c – b + a -1)
⇒x3 + ax2 + bx + (b – a + 1) = (x + 1) {x2 + (a – 1)x + (b -a+ 1)}
Let a and p be the other two zeroes of the given polynomial, then
---------------------------------
refer to attatchment #3
---------------------------
Ответ:
25.1 m squared
Step-by-step explanation:
3.14 times 8= 25.1
gotchu fam lol