Question

If \[\sqrt{5}\ \text{and} - \sqrt{5}\]   are two zeroes of the polynomial x³ + 3x² − 5x − 15, then its third zero is

पर्याय

•  3

• -3

• 5

• -5

Answer 1

Let `alpha =sqrt5 `  and `beta -sqrt5` be the given zeros and  y be the third zero of the polynomial `x^3 + 3x^2 - 5x -15`. Then,

By using `alpha + beta + y  (-text{coefficient of }x^2)/(text{coefficient of } x^3)`

`alpha + beta + y = -3 /1`

`alpha + beta + y = -3`

Substituting `alpha = sqrt5`  and `beta = -sqrt5` in `alpha + beta  + y = -3`

We get

`sqrt5 - sqrt5 + y = -3`

`cancel(sqrt5) - cancel(sqrt5) + y = -3`

` y =-3`

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