Question

If beta and alpha are the zeroes of the polynomial p(x)=6x²-5x + k,find k if 1/alpha+1/beta=5

Answer 1

Answer:

k = 1

Step-by-step explanation:

Given : p(x) = 6x² - 5x + k

On comparing with ax² + bx + c, we get

a = 6, b = - 5, c = k

Now, Sum of zeroes = α + β = - b/a

= - (- 5)/6

= 5/6

Product of zeroes = αβ = c/a

= k/6

It is given in the question that

→ (1/α) + (1/β) = 5

→ (α + β) / αβ = 5

Putting known values, we get

→ (5/6) / (k/6) = 5

→ 5/k = 5

→ k = 1