Question

if one of the zeros of the polynomial 5x²+13x-k is the reciprocal of other, find the value of k

Answer 1

Answer:

-1/5

Step-by-step explanation:

If α and β are zeros, and the polynomial is expressed as:

ax² + bx + c

For the given polynomial a = 2, b = 13 and c = -k

Then α + β = -b and αβ = ac

∵ β = 1/α, ∴ ac = αβ = 1

⇒ 5 (-k) = 1

⇒ k = -1/5