Without solving the equation 3x^2−12x+7=0 find the sum of the squares of its roots.

Step-by-step explanation:

If α + β are the roots of the equation ax² + bx + c = 0 then

(x - α)(x - β) = 0, that is

x² - x(α + β) + αβ = 0

comparing the equation with ax² + bx + c = 0 ( ie. x² + + = 0 ) then

α + β = - , αβ =

comparing 3x² - 12x + 7 = 0 with ax² + bx + c = 0, gives

a = 3, b = - 12, c = 7, hence

α + β = - = 4 and αβ =

(α + β)² = α² + β² + 2αβ

α² + β² = (α + β)² - 2αβ = 4² - =

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24

41*67/2=1373.5

step-by-step explanation:

i just used a calculator