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Question
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
Options
1
−1
2
−2
Solution
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)`
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