Question

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

Answer 1

Answer:

$\frac{34}{3}$

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 + $\frac{bx}{a}$ + $\frac{c}{a}$ = 0 ) then

α + β = - $\frac{b}{a}$ , αβ = $\frac{c}{a}$

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

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

α + β = - $\frac{-12}{3}$ = 4 and αβ = $\frac{7}{3}$

(α + β)² = α² + β² + 2αβ

α² + β² = (α + β)² - 2αβ = 4² - $\frac{14}{3}$ = $\frac{34}{3}$

Answer 2

Answer:

34/3

Step-by-step explanation:

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