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