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Question
If the zeroes of the polynomial `f(x) = x^3 – 3x^2 + x + 1` are (a – b), a and (a + b), find the values of a and b.
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Solution
By using the relationship between the zeroes of he quadratic polynomial.
We have, Sum of zeroes=`(-("Coefficient of" x^2))/("Coefficient of" x^3)`
∴ a – b + a + a + b=`-(-3)/1`
⇒ 3a = 3
⇒ a = 1
Now, Product of zeroes=`(-"(Constant term")/("Coefficient of" x^3)`
∴ (a – b) (a) (a + b)=`(-1)/1`
⇒ (1 – b) (1) (1 + b) = –1 [∵a =1]
⇒` 1 – b^2 = –1`
`⇒ b^2 = 2`
`⇒ b=+-sqrt2`
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