Question

If α and β are the zeros of 10x^2+20x-80, then the value of \(\frac {1}{\alpha } + \frac {1}{\beta }\) is _______

(a) \(\frac {5}{4}\)

(b) \(\frac {1}{5}\)

(c) \(\frac {3}{4}\)

(d) \(\frac {1}{4}\)

The question was posed to me in a national level competition.

I need to ask this question from Zeros and Coefficients of Polynomial in portion Polynomials of Mathematics – Class 10

Answer 1

Right option is (d) \(\frac {1}{4}\)

For explanation: \(\frac {1}{\alpha } + \frac {1}{\beta } = \frac {\alpha +\beta }{\alpha \beta }\)

α+β=\(\frac {-20}{10}\)=-2

αβ=\(\frac {-80}{10}\)=-8

∴ \(\frac {\alpha +\beta }{\alpha \beta } = \frac {-2}{-8} = \frac {1}{4}\)