Question

If the one root of 5x²+13x+k =0 is reciprocal of the other root ,then find value of k.

Answer 1

5

Explanation:

Let x₁ = n → x₂ =
`(1)/(n)`

equation:
`a(x-n)(x-(1)/(n) )=0`

∴
`a(x-n)(x-(1)/(n) )=5x^2+13x+k`

`a(x^(2) -(n+(1)/(n) )x+1)= 5(x^(2) +(13)/(5) x+(k)/(5) )`

• 
  `a=5`
• 
  `-(n+(1)/(n) )=(13)/(5)`
• 
  `1=(k)/(5)` → k = 5