Question

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

A. \(\frac{7}{3}\)

B. - \(\frac{7}{3}\)

C. \(\frac{3}{7}\)

D. - \(\frac{3}{7}\)

Answer 1

Given,

p(x) = 4x² + 3x + 7

α + β = – b/a

= – 3x/4x² = – 3/4x ………. (i)

αβ = c/a

= 7/4x² …………. (ii)

Dividing (i) from (ii),

We get,

So,

1/α + 1/β = – 3/7