Question

If alpha , beta are the roots of 2x²-4x+5=0 the 1/alpha+1/beta is​

Answer 1

Answer:

Given: α,β are the roots of the equation 2x

2

+4x−5=0

To find the equation whose roots are the reciprocals of 2α−3,2β−3

Sol: From the given criteria, x=α,β

Let y=2x−3⟹x=

2

y+3

Now put value of x in the given equation, we get

2(

2

y+3

)

2

+4(

2

y+3

)−5=0

⟹2(y

2

+6x+9)+8y+24−20=0×4

⟹2y

2

+20y−22=0

⟹y

2

+10y−11=0

i.e., the equation whose roots are the reciprocals of 2α−3,2β−3 is x

2

+10x−11=0

Step-by-step explanation:

Hope it will be helpful.