. If and are the zeroes of quadratic polynomial f(x) = kx2 +4x + 4 such that 2 + 2 = 24,
find the value of k.
Answers
Answer:
Step-by-step explanation:
Some error in your question , question is in such a way --> α and β are the zero of the Kx² + 4x + 4 , α² + β² = 24 then find k ?
Solution :- α and β are the zeros of the given polynomial Kx² + 4x + 4 = 0
so, product of zeros = αβ = constant/coefficient of x² = 4/K
sum of zeros = α + β = -coefficient of x/Coefficient of x² = -4/k
Now, α² + β² = 24
⇒(α + β)² - 2αβ = 24
⇒(-4/k)² - 2(4/k) = 24
⇒16/K² - 8/k = 24
⇒ 2 - k = 3k²
⇒3k² + k -2 = 0
⇒ 3k² + 3k - 2k - 2 = 0
⇒3k(k + 1) - 2(k +1) = 0
⇒(3k -2)(k + 1) = 0
Hence, k = 2/3 and -1
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