Notifications
Clear all
If the zeroes of the polynomial x^3  3x^2+ x + 1 are a – b, a, a + b, find a and b.
Polynomials
1
Posts
2
Users
0
Likes
179
Views
0
25/05/2021 1:17 pm
Topic starter
If the zeroes of the polynomial x^{3 } 3x^{2}+ x + 1 are a – b, a, a + b, find a and b.
Answer
Add a comment
Add a comment
Topic Tags
1 Answer
0
25/05/2021 1:18 pm
We are given with the polynomial here,
p(x) = x^{3}3x^{2}+x+1
And zeroes are given as a – b, a, a + b
Now, comparing the given polynomial with general expression, we get;
∴ px^{3}+qx^{2}+rx+s = x^{3}3x^{2}+x+1
p = 1, q = 3, r = 1 and s = 1
Sum of zeroes = a – b + a + a + b
q/p = 3a
Putting the values q and p.
(3)/1 = 3a
a=1
Thus, the zeroes are 1b, 1, 1+b.
Now, product of zeroes = 1(1b)(1+b)
s/p = 1b^{2}
1/1 = 1b^{2}
b^{2} = 1+1 = 2
b = √2
Hence,1√2, 1, 1+√2 are the zeroes of x^{3} 3x^{2 }+x +1.
Add a comment
Add a comment
Forum Jump:
Related Topics

If two zeroes of the polynomial x^46x^326x^2+138x35 are 2 ±√3, find other zeroes.
2 years ago

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.
2 years ago

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: x^3 4x^2+ 5x2; 2, 1, 1
2 years ago

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: 2x^3+x^25x+2; 1/2, 1, 2
2 years ago

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0
2 years ago
Forum Information
 321 Forums
 27.1 K Topics
 53.3 K Posts
 0 Online
 16.7 K Members
Our newest member: Stripchat
Forum Icons:
Forum contains no unread posts
Forum contains unread posts
Topic Icons:
Not Replied
Replied
Active
Hot
Sticky
Unapproved
Solved
Private
Closed
Super Globals
Requests: Array ( )
Server: Array ( )