Question

If one root of the polynomial f(x) = 5x² + 13x + k is reciprocal of the other, then the value of k is

विकल्प

• 0

• 5

• \[\frac{1}{6}\]

• 6

Answer 1

If one zero of the polynomial f(x) = 5x² + 13x + k  is reciprocal of the other. So  `beta = 1/alpha ⇒`

Now we have

`alphaxxbeta= (\text{Constant term})/(\text{Coefficient of}x^2)`

`= k /5`

Since`alphabeta =1` 

Therefore we have

`alpha beta = k/5`

`1= k/5`

`⇒ k = 5`

Hence, the correct choice is `(b)`.