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givi [52]
3 years ago
6

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

Mathematics
1 answer:
Contact [7]3 years ago
4 0

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}

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