Question

If alpha and beta are the zeroes of the polynomial p(x)=6x^(2)+5x-k satisfying the relation alpha-beta=(1)/(6) then find the value of k .
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Answer 1

Answer:

k = -16

Step-by-step explanation:

p(x) = 6x² + 5x - k

Given that α - β = 1/6

Here α + β = -b/a = -5/6

αβ = c/a = -k/6

(α - β)² = α² + β² - 2αβ

α² + β² can be expressed as (α + β)² - 2 αβ

Substituting the values, we get

(α - β)² = (α + β)² - 2 αβ - 2 αβ

=> (1/6)² = ( -5/6)² - 4αβ

1/36 = 25/36 - 4αβ

=> 4αβ = (25/36) - (1/36) = 24/36

Therefore αβ = ¼ of 24/36 = 24/9 = 8/3

Given that αβ = c/a = 8/3

-k/6 = 8/3

Equalising the denominators, we get

-k/6 = 16/6

So, K = -16