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Question
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
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Solution
f(x) = ax2 + bx + c
α + β = `(-b/a)`
αβ = `c/a`
since α + β are the roots (or) zeroes of the given polynomials
then
α - β
The two zeroes of the polynomials are
`(-b+sqrt(b^2-4ac))/(2a)-((-b-sqrt(b^2-4ac))/(2a))=(-b+(sqrt(b^2-4ac)+b+sqrt(b^2-4ac)))/(2a)=(2sqrt(b^2-4ac))/(2a)=(sqrt(b^2-4ac))/a`
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