Question

If α, β are the roots of x^2 + 3x + 3 = 0, then find the quadratic equation whose roots are α+β and αβ.

Answer 1

Answer:

Correct option is

C

3x

2

−2x+1=0

Let α,β are roots of x

2

−2x+3=0

Then α+β=2;αβ=3.

Now

α+1

α−1

+

β+1

β−1

=

(α+1)(β+1)

(α−1)(β+1)+(α+1)(β−1)

=

αβ+α+β+1

αβ+α−β−1+αβ−α+β−1

=

αβ+α+β+1

2αβ−2

=

3+2+1

6−2

=

6

4

=

3

2

(

α+1

α−1

)(

β+1

β−1

)=

(αβ+α+β+1)

αβ−α−β+1

=

3+2+1

3−2+1

=

6

2

=

3

1

Hence, equation is x

2

−(

3

2

)x+(

3

1

)=0⇒3x

2

−2x+1=0.