This is also an important question of class 10th. Please help me for solving this question. This optional exercise also an important exercise of class 10th. How i solve easily please help me for this question If the zeroes of the polynomial x3-3×2+x+1 are a – b, a, a + b, find a and b

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# If the zeroes of the polynomial x3-3×2+x+1 are a – b, a, a + b, find a and b.Q.3

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We are given with the polynomial here,

p(x) = x

^{3}-3x^{2}+x+1And 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+1p = 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-b

^{2}-1/1 = 1-b

^{2}b

^{2}= 1+1 = 2b = √2

Hence,1-√2, 1 ,1+√2 are the zeroes of x

^{3}-3x^{2}+x+1.