Question

HEYA GUYS
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If alpha , beta are zeros of quadratic polynomial kx^2 + 4x + 4 find the value of k such that ( alpha + beta )^2 -- 2 alpha beta = 24​

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