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If the zeroes of the polynomial x 3 – 3x 2 + x + 1 are a – b, a, a + b, then find the value of a and b

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3 months ago

Anand Kumar Pandey
2803 Points
```							Dear StudentLet the given polynomial be:p(x) = x^3– 3x^2+ x + 1Given,The zeroes of the p(x) are a – b, a, and a + b.Now, compare the given polynomial equation with general expression.px^3+ qx^2+ rx + s = x^3– 3x^2+ x + 1Here, p = 1, q = -3, r = 1 and s = 1For sum of zeroes:Sum of zeroes will be = a – b + a + a + b-q/p = 3aSubstitute the values q and p.-(-3)/1 = 3aOr,a = 1So, the zeroes are 1 – b, 1, 1 + b.For the product of zeroes:Product of zeroes = 1(1 – b)(1 + b)-s/p = 1 – 𝑏^2=> -1/1 = 1 – 𝑏^2Or, 𝑏^2= 1 + 1 =2So,b = √2Thanks
```
3 months ago
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