Question

If a – b, a and a + b are the zeroes of the polynomial f(x) = x
^3 – 3x^2+x + 1, then the values of a and b respectively are​

Answer 1

Answer:

a=1 and b=√2

Step-by-step explanation:

Given : f(x)=x³-3x²+x+1 and (a-b) , a , (a+b) are the zeroes of f(x)

As we know , sum of zeroes = (a-b)+a+(a+b) = -b/a = 3

So, 3a = 3

Hence, a=1

Now, sum of product of zeroes = (a-b)a + (a+b)a + (a-b)(a+b) = c/a = 1

So, a²-ab+a²+ab+a²-b² = 1

      3a²-b² = 1    

Now putting a=1  , 3(1)²-b² = 1

                             3 - b²= 1

                             3 - 1 = b²

                             b² = 2

Hence , b = √2