The roots of the equation $3{{x}^{2}}-2kx+k+4=0$ are $\alpha $ and $\beta $. If \({{\alpha }^{

Question

The roots of the equation $3{{x}^{2}}-2kx+k+4=0$ are $\alpha $ and $\beta $. If ${{\alpha }^{2}}+{{\beta }^{2}}=\frac{16}{9}$, find the possible values of $k$.

Accepted Answer

Formal candidates: $k=4$ or $k=-\frac52$. If the roots must be real, only $k=-\frac52$, since $D=-32$ for $k=4$.

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Solution:

Solution locked