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Question
If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 − 4x + 9 is 3, then its third zero is
Options
- \[\frac{3}{2}\]
- \[- \frac{3}{2}\]
- \[\frac{9}{2}\]
- \[- \frac{9}{2}\]
Solution
Let αβγ be the zeros of polynomial f(x) = 2x3 + 6x2 − 4x + 9 such that `alphabeta=3`
We have,
`alpha ß y= - (text{coefficient of x})/(text{coefficient of } x^2)`
`=(-9)/2`
Putting `alphabeta` in `alpha beta y`, we get
`alpha beta y = (-9)/2`
`3 y = (-9)/2xx1/3`
`y = (-3)/2`
Therefore, the value of third zero is `(-3)/2`
Hence, the correct alternative is (b).
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