Math, asked by ntalwar08102005, 5 hours ago

if alpha and beta are the zeros of the polynomial f(x)=ax2+bx+c then evaluate root b^2-4ac/c

Answers

Answered by jeemitvpandya
0

Answer:

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

f(x)=ax

2

+bx

2

+c

aα+b

β

+

aβ+b

α

=

(aα+b)(aβ+b)

β(aβ+b)+α(aα+b)

=

a

2

αβ+abαabβ+b

2

2

+bβ+aα

2

+bα

=

a

2

(αβ)+ab(α+β)+b

2

a(α

2

2

)+b(α+β)

observe, we have

α+β=

a

−b

αβ=

a

c

⇒ α

2

2

=(α+β)

2

−2αβ

=

a

2

b

2

a

2c

Using equations on the right

=

a

2

(

a

c

)+ab(

a

−b

)+b

2

a(

a

2

b

2

a

2c

)+b(

a

−b

)

=

ac−b

2

+b

2

a

b

2

−2c−

a

b

2

=

ac

−2c

=

a

−2

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