Question

if the zeros of the polynomial f(x)=x³-3x²+x+1 are a-b, a+b find a

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Answer 1

Answer:

a=1 and b = (± √2)

Step-by-step explanation:

a−b,a,a+b are zeroes of x³-3x²+x+1

⇒a−b+a+a+b= sum of zeroes = 3

⇒3a=3

⇒a=1

(a−b)(a)(a+b)= product of zeroes =−1

⇒(1−b)(1+b) = (−1)

⇒1−b² = (−1)

⇒b² = 2

⇒b = (± √2)