If the zeros of the polynomial x^3 -3x^2+x+1 are a-b , a, a+b, find a and b.
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1
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Answer:
p(x)=x^3-3x^2+x+1(Ax^3+Bx^2+CX+D)
let alpha be a-b,
let beta be a,
let gamma be a+b
We know that,
alpha +beta+gamma=-B/A. (put the value)
then,
a-b+a+a+b=-(-3)/1
3a=3/1
a=1
alpha*beta*gamma=-D/A
(a-b)(a)(a+b)=-1
l-b^2=-1
b^2=2
b=+-√2
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