Question

The roots of the equation 2x2

– 7x + 5 = 0 are α and β. Without solving for the roots, find

α
/
β

=

β
/
α

.​

Answer 1

Answer:

ANSWER

2x

2

−7x+8=0

α,β are roots of above equation (ax

2

+bx+c=0)

∴α+β=

a

−b

=

2

7

-(1)

αβ=

2

8

(

a

c

)=4

Roots of other eq

n

⇒(3α−4β),(3β−4α)

⇒ sum of roots = 3α−4β+3β−4α

=−α−β=−(α+β)

=(−

2

7

) (from (1))

⇒ product of roots ⇒(3α−4β)(3β−4α)

=9αβ−12α

2

−12β

2

+16αβ

=25αβ−12(α

2

+β

2

)

=25αβ−12((α+β)

2

−2αβ)

=25αβ−12(α+β)

2

+21αβ

=49αβ−12(α+β)

2

⇒49(4)−12(

2

7

)

2

⇒49(4)−12×

4

49

=49(4−3)

⇒(49)

⇒ quadratic poly ⇒x

2

- (sum of roots)x+(product of roots)

⇒x

2

−(

2

−7

)x+49

⇒2x

2

+7x+98 (option A)