Question

If α,β are the roots of the equation 4x² + 3x + 7 = 0, then the value of $\frac{1}{\alpha^{3}} + \frac{1}{\beta^{3}}$is equal to –

• A. – $\frac{27}{64}$
• B. $\frac{63}{16}$
• C. $\frac{225}{343}$
• D. None of these

Answer 1

Answer: (C)

$\frac{225}{343}$

Answer 2

α + β = – 3/4, αβ = 7/4

$\frac{1}{\alpha^{3}} + \frac{1}{\beta^{3}}$= $\frac{(\alpha + \beta)^{3} - 3\alpha\beta(\alpha + \beta)}{\alpha^{3}\beta^{3}}$

= $\frac{( - 3/4)^{3} - 3.(7/4.)( - 3/4)}{(7/4)^{3}}$= $\frac{225}{343}$