Question

If $a$ and $b$ are the roots of the quadratic equation ${3x}^2+8x+2=0$, find the value of $a^3+b^3$.

• A. $\frac{368}{27}$
• B. $\frac{-368}{27}$
• C. $\frac{-368}{24}$
• D. None of these

Answer 1

The correct option is B $\frac{-368}{27}$

Given equation is: $3x^2+8x+2=0$

$a$ and $b$ are the roots of the equation.

$\therefore a+b=\frac{8}{3}$ and $ab=\frac{2}{3}$

$a^3+b^3={(a+b)}^3-3ab(a+b)$
$={\left(\frac{8}{3}\right)}^3-3\times \frac{2}{3}\times \frac{8}{3}$

$=\frac{512}{27}-\frac{16}{3}$

$=\frac{-368}{27}$