Without solving the equation 3x2-12x+7=0 find the sum of the squares of its roots.

Step-by-step explanation:

3x²-12x+7=0

x = (-b ± √ b²-4ac) / 2a

from these equation: a = 3, b = 12, c = 7

Accordingly, b² - 4ac = 12² - 4 (3 x 7) = 144 - 4 (21) = 144 - 84 = 60

2a = 2 x 3 = 6

Applying the quadratic formula:

x = (-12 ± √ 60) / 6

√ 60 rounded to 2 decimal digit using calculator 7.75

x = (-12 ± 7.75) / 6

(-12 ± 7.75) = (-12 + 7.75) = 5.75

(-12 - 7.75) = - 19.75

x = 5.75/6 = 0.96

-19.75/6 = 3.29

sum of the square of roots = 0.96² + 3.29²

0.9261 + 10.8241 = 11.75