Forum

If the zeroes of th...
 
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.

1 Posts
2 Users
0 Likes
251 Views
0
Topic starter

If the zeroes of the polynomial x3 - 3x2+ x + 1 are a – b, a, a + b, find a and b.

1 Answer
0

We are given with the polynomial here,

p(x) = x3-3x2+x+1

And zeroes are given as a – b, a, a + b

Now, comparing the given polynomial with general expression, we get;

∴ px3+qx2+rx+s = x3-3x2+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 1-b, 1, 1+b.

Now, product of zeroes = 1(1-b)(1+b)

-s/p = 1-b2

-1/1 = 1-b2

b2 = 1+1 = 2

b = √2

Hence,1-√2, 1, 1+√2 are the zeroes of x3- 3x2 +x +1.

Share:

How Can We Help?