Question

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

Answer 1

Answer:

ANSWER

If α and β are roots / zero of the quadratic equation 

f(x)=ax2+bx2+c

aα+bβ+aβ+bα

=(aα+b)(aβ+b)β(aβ+b)+α(aα+b)

=a2αβ+abαabβ+b2aβ2+bβ+aα2+bα

=a2(αβ)+ab(α+β)+b2a(α2+β2)+b(α+β)

observe, we have

α+β=a−b

αβ=ac

⇒ α2+β2=(α+β)2−2αβ

=a2b2−a2c

Using equations on the right

=a2(ac)+ab(a−b)+b2a(a2b2−a2c)+b(a−b)

=ac−b2+b2ab2−2c−ab2

=ac−2c=a−2

____________________________________________