Question

if alpha and beta are the roots of ax^2+bx+c=0 then find the value of (alpha^2-beta^2)+(beta^2-alpha^2)
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Answer 1

Answer:

the answer becomes alpha plus beta as we know it is -b/a

Answer 2

Answer:

=b²/a⁴ (b²-4ca)

Step-by-step explanation:

α and β are the roots of ax²+bx+c=0

αβ=c/a and α+β=-b/a

Now  (α²-β²)(β²-α²)

= - (α²-β²)²

=-(α+β)²(α-β)²

=-(α+β)²{ (α+β)²-4αβ }

Plugging the values of αβ=c/a and α+β=-b/a

=(-b/*a)² { (-b/a)²-4(c/a)}

= b²/a² { b²/a²-4c/a)

=b²/a⁴ (b²-4ca)