Question

If alpha and beta are the zeroes of the quadratic polynomial p(x)=ax2+bx+c then evaluate alpha minus beta.

Answer 1

let alfa be A and beta be B
then,
A+B=(-b/a)
AB=c/a
So,A-B=_/((A-B)^2)
=>_/(A^2+B^2+2AB)
=>_/((A+B)^2-4AB)
=>_/(b^2/a^2 - 4c/a)
=>_/((b^2-4ac)/a^2)
=>(_/(b^2-4ac))/ |a| (mod a means positive a)

PLZ MARK IT AS BRAINLIEST..

Answer 2

α + β = -b/a

αβ = c/a

We have to find α - β

[α - β ]² = [ α + β ] ² - 4αβ

= [ -b/a ]² - 4 × c/a

= b²/a² - 4c/a

= b² - 4ac /a²

α - β = √[ b² - 4ac /a² ]

= √[ b² - 4ac /a ]