Question

if the zeros of the quadratic polynomial x^2 + (a+1) +b are 2 and -3​

Answer 1

Answer:α,β are the zeros of the quadratic polynomial f(x)=ax²+bx+c

then , α+β=-b/a and α×β=c/a

a(α²/β+β²/α)+b(α/β+β/α)

=a(α³+β³)/αβ+b(α²+β²)/αβ

=a{(α+β)³-3αβ(α+β)}/αβ+b.{(α+β)²-2αβ}/αβ

=a{(-b/a)³-3c/a(-b/a)}/(c/a)+b{(-b/a)²-2c/a}(c/a)

=a²{(-b³/a³)+3bc/a²}/c+ab{(b²/a²)-2c/a}/c

=(-b³/a+3bc)/c+(b³/a-2bc)/c

=(-b³a+3bc+b³a-2bc)/c

=bc/c

=b

Step-by-step explanation: