Question

If alpha and bita are zeros of polynomial kx2+4x+4 such that a2+b2=24 find k

Answer 1

Answer:

Step-by-step explanation:

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 + 6k - k - 2 = 0

⇒3k(k + 2) - 1(k +2) = 0

⇒(3k -1)(k +2) = 0

Hence, k = 1/3 and -2

Answer 2

Here is your answer.

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