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If the zeroes of the polynomial x^3  3x^2+ x + 1 are a – b, a, a + b, find a and b.
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25/05/2021 1:17 pm
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If the zeroes of the polynomial x^{3 } 3x^{2}+ x + 1 are a – b, a, a + b, find a and b.
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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.
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