.If the zeroes of the polynomial are 3x2 − 5x + 2 are a+ b and a- b, find a and b.
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(x) = (x-(a-b))*(x-a)*(x-(a+b))
= x^3 - (a-b+a+a+b)*x^2 + (a*(a+b)+(a-b)*(a+b)+(a-b)*a)*x - (a-b)*a*(a+b)
= x^3 - 3*a*x^2 + (a*(a+b+a-b) + a^2 - b^2)*x - a*(a^2-b^2)
but p(x) = x^3-3*x^2+x+1
-3*a = -3 => a = 1
a*(a+a) + a^2 - b^2 = 1 => 2 + 1 - b^2 = 1
- a*(a^2-b^2) = 1 => -1+b^2 = 1
= x^3 - (a-b+a+a+b)*x^2 + (a*(a+b)+(a-b)*(a+b)+(a-b)*a)*x - (a-b)*a*(a+b)
= x^3 - 3*a*x^2 + (a*(a+b+a-b) + a^2 - b^2)*x - a*(a^2-b^2)
but p(x) = x^3-3*x^2+x+1
-3*a = -3 => a = 1
a*(a+a) + a^2 - b^2 = 1 => 2 + 1 - b^2 = 1
- a*(a^2-b^2) = 1 => -1+b^2 = 1
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