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