Question

if alpha and beta are the zeros of the quadratic equation FX =
$k^{2}$
+ 4 x + 4 and
${ \alpha }^{2} + { \beta }^{2}$
is equal to 24 then find the value of k​

Answer 1

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

Read more on Brainly.in - https://brainly.in/question/3180449#readmore