Question

if α and β are the zeroes of the polynomial f(x)=2x²+5x+k,satisfying the relation α²+β²+αβ=21÷4,then find the value of k,for this is to be possible.

Answer 1

α and β are the zeroes 
f(x)=2x²+5x+k
α²+β²+αβ=21÷4
α²+β²+αβ=(α+β)²-αβ
α+β= -b/a = -5/2
αβ=c/a = k/2
α²+β²+αβ=(-5/2)²-k/2
              =25/4-k/2
α²+β²+αβ=21/4
21/4=25/4-k/2
21/4-25/4=k/2
-4/4=k/2
-1=k/2
k=-1×2
k=-2

Answer 2

Answer:

Step-by-step explanation:

α and β are the zeroes  

f(x)=2x²+5x+k

α²+β²+αβ=21÷4

α²+β²+αβ=(α+β)²-αβ

α+β= -b/a = -5/2

αβ=c/a = k/2

α²+β²+αβ=(-5/2)²-k/2

             =25/4-k/2

α²+β²+αβ=21/4

21/4=25/4-k/2

21/4-25/4=k/2

-4/4=k/2

-1=k/2

k=-1×2

k=-2