Question

If two zeros x³ + x² − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is

पर्याय

•  1

• −1

• 2

• −2

Answer 1

Let `alpha = sqrt5` and `beta= -sqrt5` be the given zeros and y  be the third zero of x³ + x² − 5x − 5 = 0 then

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

`alpha + beta + y = (+(+1))/1`

`alpha + beta + y = -1`

By substituting `alpha = sqrt5` and `beta= -sqrt5` in `alpha +beta+y = -1`

`cancel(sqrt5) - cancel(sqrt5) + y = -1`

` y = -1`

Hence, the correct choice is`(b)`