Question

If α + β = 3 and $\alpha^{3}$ + [tex]\beta^{3} = 7, then α and β are roots of equation :
a) 9$x^{2}$ + 27x + 20 = 0
b) 9$x^{2}$ - 27x + 20 = 0
c) 9$x^{2}$ + 27x - 20 = 0
d) 9$x^{2}$ - 27x - 20 = 0

Answer 1

Answer:

Step-by-step explanation:

Solution

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Given, α+β=3

and α  

3

+β  

3

=7

⇒(α+β)(α  

2

+β  

2

−α.β)=7

⇒(α+β)  

2

−3αβ=  

3

7

​

 

⇒9−  

3

7

​

=3αβ

⇒αβ=  

9

20

​

 

Hence quadratic equation having roots α,β is given by, 9x  

2

−27x+20=0