Question

if a and b are the zeros of the polynomial x^+4x+4k such that a^+ b^ =24 then find k​

Answer 1

Step-by-step explanation:

α,β roots of f(x)=kx

2

+4x+4

Given α

2

+β

2

=24

We know α+β=

a

−b

=

k

−4

αβ=

a

c

=

k

4

(α+β)

2

=α

2

+β

2

+2αβ

(

k

−4

)

2

=24+2(

k

4

)

k

2

4

2

=24+2(

k

4

)

16=24k

2

+8k

2=3k

2

+k

0=3k

2

+k−2

0=3k

2

+3k−2k−2

0=3k(k+1)−2(k+1)

0=(k+1)(3k−2)

∴k=−1,

3

2