Question

34- Ifa, ß are the roots of the equation x2-5x+k=0, then what is the value of k such that
a-ß=1​

Answer 1

Answer:

Here goes the solution!

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=1^2

⇒ 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.

Answer 2

Step-by-step explanation:

x^5 - 5x + k=0.

from equation ( Alpha - beta = 1 )

Alpha = beta + 1. _eqn1

sum of roots

alpha + beta = -b

a

putting the value of Alpha from eqn1

beta + 1 + beta = - ( -5 )

1

2beta + 1 = 5

2beta = 4

beta = 2

from equation first

then alpha = 3

product of roots

Alpha × beta = c/ a

3×2= k/1

6= k