Question

If x2 + 5x + 6 + k = 0, then the value of k for
which roots of the given equation differ by 1 is
​

Answer 1

α + β = - 5

α - β = 1

2 α = -4

α = -2 and β = -3

αβ = (6+k)

6 = 6 + k

So, k = 0

Answer 2

Answer:

Step-by-step explanation:

Let  

r

r

and  

r+2

r+2

be the roots.

Their sum is  

r+(r+2)=

−5

3

r+(r+2)=−53

thus

r=

−11

6

.

r=−116.

Their product is

r(r+2)=

−k

3

.

r(r+2)=−k3.

thus  

k=

11

12

k=1112

the roots are  

−

11

6

−116

and  

1

6