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प्रश्न
If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\] is equal to
विकल्प
- \[\frac{7}{3}\]
- \[- \frac{7}{3}\]
- \[\frac{3}{7}\]
- \[- \frac{3}{7}\]
उत्तर
Since `alpha` and ß are the zeros of the quadratic polynomial p(x) = 4x2 + 3x + 7,
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`= (-3)/4`
`alpha ß = (\text{constat term})/(text{coefficient of} x^2)`
`= 7/4`
We have
`= 1/alpha + 1/ ß `
`= (ß + alpha )/(alpha ß )`
`= (-3)/(4/7)`
`= (-3)/4 xx4/7`
`= (-3)/cancel(4)xxcancel(4)/7`
`= (-3)/7`
The value of `1/alpha +1/beta` is `(-3)/7`
Hence, the correct choice is `(d)`
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