Answer:
-56/9
Step-by-step explanation:
Let p and q be the roots of the equation.
So, here's how we're gonna work it out:
[tex] {p}^{2} + {q}^{2} = \\ {p}^{2} + {q}^{2} +2 pq - 2pq = \\ ( {p}^{2} +2pq + {q}^{2}) - 2pq = \\ {(p + q)}^{2} - 2pq[/tex]
Vieta's formulas give us the sum and the product of the roots of a quadratic equation. Using them we obtain:
[tex] {(p + q)}^{2} - 2pq = \\ {( - \frac{ 4}{3} )}^{2} - 2 \times 4 = \frac{16}{9 } - 8 = \\ \frac{16 - 72}{9} = - \frac{56}{9} [/tex]
