If the zeroes of the polynomial x^3 - 3x^2+ x + 1 are a – b, a, a + b, find a and b.
25/05/2021 1:17 pmTopic starter
If the zeroes of the polynomial x3 - 3x2+ x + 1 are a – b, a, a + b, find a and b.
25/05/2021 1:18 pm
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
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.