Question

Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0

Answer 1

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:

${p}^{2} + {q}^{2} = \\ {p}^{2} + {q}^{2} +2 pq - 2pq = \\ ( {p}^{2} +2pq + {q}^{2}) - 2pq = \\ {(p + q)}^{2} - 2pq$

Vieta's formulas give us the sum and the product of the roots of a quadratic equation. Using them we obtain:

• p + q = -b / a = - 4 / 3
• p × q = c / a = 12 / 3 = 4

${(p + q)}^{2} - 2pq = \\ {( - \frac{ 4}{3} )}^{2} - 2 \times 4 = \frac{16}{9 } - 8 = \\ \frac{16 - 72}{9} = - \frac{56}{9}$