Question

Sum of the cubes of the roots of the quadratic equation ${3x}^2-5x+2=0$

• A. $-\frac{35}{27}$
• B. $\frac{7}{9}$
• C. $\frac{27}{35}$
• D. $\frac{35}{27}$

Answer 1

Answer: (D)

$\frac{35}{27}$

Given equation is: $3x^2-5x+2=0$

$\therefore a=3,b=-5,c=2$

Let $\alpha$ and $\beta$ be the roots of the equation.

$\therefore \alpha +\beta =\frac{5}{3},\alpha \beta =\frac{2}{3}$

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

$={\left(\frac{5}{3}\right)}^3-3\times \frac{2}{3}\times \frac{5}{3}$

$=\frac{125}{27}-\frac{10}{3}=\frac{35}{27}$