Question

The sum of all the value of $m$ for which the roots $x_1$ and $x_2$ of the quadratic equation $x^2-2 m x+m=0$ satisfy the condition $x_1^3+x_2^3=x_1^2+x_2^2$, is

• A. $\frac{3}{4}$
• B. 1
• C. $\frac{9}{4}$
• D. $\frac{5}{4}$

Answer 1

Answer: (D)

$ x_1+x_2=2 m ; x_1 x_2=m$
$\left(x_1+x_2\right)^3-3 x_1 x_2\left(x_1+x_2\right)=\left(x_1+x_2\right)^2-2 x_1 x_2 $
$8 m^3-3 m(2 m)=4 m^2-2 m$
$8 m^3-10 m^2+2 m=0 \Rightarrow m_1+m_2+m_2=\frac{10}{8}=\frac{5}{4} $