if a and b are the zeros of the polynomial x^+4x+4k such that a^+ b^ =24 then find k
Answers
Answered by
0
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
Similar questions