if alpha and beta are the zeros of the quadratic polynomial x is equal to X square + 4 x + K such that Alpha square plus beta square + alpha beta equal 21 upon 4 the value of k is .
Answers
Answered by
4
Answer:
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