Question

28. If α and β are zeroes of x2 + 5x + 5, find the value of α^-1 + β^-1​

Answer 1

given quadratic polynomial is:

x² + 5x + 5

comparing it with

ax² + bx + c

we will get,

a = 1 ; b = 5 ; c = 5

we know that,

sum of zeroes ( α + β ) = -b / a = -5 / 1 = -5   ----------eqn(1)

product of zeroes ( α β ) =  c / a = 5 / 1 = 5  ----------eqn(2)

we have to find

α ⁻¹ + β ⁻¹  

that is,

1 / α + 1 /β

taking LCM we get

( α + β ) / αβ

( putting values by eqn (1) and (2) )

= -5 / 5

= -1

so,

value of α ⁻¹ + β ⁻¹  = - 1

Answer 2

Answer:

x2-5x+k

Here, a=1, b=-5 and c=k

Now, α+ β = -b/a= -(-5)/1= 5

α*β = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4k=1

⇒ -4k= 7-25

⇒ -4k= -24

⇒ k=6 So the value of k is 6.