Question

If α, β are the zeros of the polynomial p(x) = 4x² + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\]  is equal to

Options

• \[\frac{7}{3}\]
• \[- \frac{7}{3}\]
• \[\frac{3}{7}\]
• \[- \frac{3}{7}\]

Answer 1

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)`