Question

11) As raízes da função quadrática f(x) = x²-5x+6 são: 

A)0 e 2

B)1 e 2

C)2 e 4

D)2 e 3

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Answer 1

Para saber as raízes de uma função você deve igualar f(x) = y = 0.

$\displaystyle f(x) = x^2-5x+6\\0 = x^2-5x+6\\\\\\x=\frac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-5)\pm\sqrt{(-5)^2-4.1.6}}{2.1}\\\\x=\frac{5\pm\sqrt{25-24}}{2}\\\\x=\frac{5\pm\sqrt{1}}{2}\\\\x=\frac{5\pm 1}{2}\\\\\\x' = \frac{5+1}{2}=\frac{6}{2}=3\\\\x''=\frac{5-1}{2}=\frac{4}{2}=2$

Portanto, as raízes são x' = 3 e x'' = 2.

Alternativa D.