Question

2 points

IF α & β are the roots of the the quadratic equation 3m² + 2m- 4 = 0 then α²+ β²

​

Answer 1

....................

Answer 2

Answer:

Given that α,β are the roots of equation ax

2

+bx+c=0

So we have α+β=−

a

b

and αβ=

a

c

1.

α

2

1

+

β

2

1

=

(αβ)

2

α

2

+β

2

=

(αβ)

2

(α+β)

2

−2αβ

=

c

2

b

2

−2ca

2. α

4

β

7

+α

7

β

4

=(αβ)

4

(α

3

+β

3

)

=(αβ)

4

(α+β)(α

2

+β

2

−αβ)

=

a

4

c

4

×(−

a

b

)×(

a

2

b

2

−3ac

)

=

a

7

bc

4

(3ac−b

2

)

3. (

β

α

−

α

β

)

2

=(

αβ

(α+β)(α−β)

)

2

=

c

2

b

2

×(

a

2

b

2

−4ac

)