Question

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β

Answer 1

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`