Let \(a,b,c\) and \(d\) be the roots of \(x^4 + 8x^3 + 9x^2 + 5x + 4 = 0.\) Find the value of \(\frac{1}{ab} + \frac{1}{ac} + \frac{1}{ad} + \frac{1}{bc} + \frac{1}{bd} + \frac{1}{cd}.\)

Try making the expression you're trying to find into one big fraction. Then use Vieta's Formulas and plug coefficients in.

Let P be the value of the required expression.

\(P = \dfrac{cd+bd+bc+ad+ac+ab}{abcd} = \dfrac{\dfrac{9}{1}}{\dfrac{4}{1}} = \dfrac{9}{4}\)