Answer to Question #2436 in Algebra for shivam

Question

If one of the zeroes of the polynomial 5x2 + 13x +k is reciprocal of the other, then
find the value of k.

Answer 1

5x² + 13x + k = 0
D = 169 - 20k
x₁ = (-13 + √(169 - 20k))/10
x₂ = (-13 - √(169 - 20k))/10

x₁ = 1/x₂
(-13 + √(169 - 20k))/10 = 10/ (-13 - √(169 - 20k))
100 = (-13 + √(169 - 20k))(-13 - √(169 - 20k)) = 169 - 169 + 20k = 20k
k = 10.