Question

22. Determine the range of values of real constant k for which the cubic 2x³- 9x²+ 12x-k=0
has all roots real.​

Answer 1

Answer:

Step-by-step explanation:

2x³- 9x²+ 12x-k=0

α , α, β are the real roots

2α + β =9/2 , α²β =  k/2

α² + αβ +βα = 12/2

α² + 2αβ =6

β = 9/2 -2α

α² +2α(9/2 -2α)=6

α²+9α -4α² = 6

- 3 α² + 9α -6 =0

-3α² +6α + 3α -6 =0

-3α (α - 2) + 3 (α-2) = 0

3 (α-1 ) (α -2)=0

α = 1 , β = 1/2

Answer 2

Answer:

range = (4,5)

Step-by-step explanation:

See attached image