Question

qual a soma das raizes da função f(x)= x²-6x+4?

Answer 1

Soma = -b/a
S = -(-6)/1
S = 6

Answer 2

$f(x) = x^2 - 6x + 4$

Resolvendo por Bháskara.

$x = \dfrac{-b \pm \sqrt{b^2 -4*a*c}}{2*a}$

$x^{2} - 6x + 4 = 0$

a=1, b=−6, c=4
Δ=b²−4ac
Δ=(−6)2−4*(1)*(4)
Δ=36−16
Δ=20

$x = \dfrac{-b \pm \sqrt{\triangle}}{2*a}$

$x = \dfrac{-(-6) \pm \sqrt{20}}{2*1} \\ \\ \\ x = \dfrac{6 \pm 2\sqrt{5}}{2} \\ \\ \\ x' = \dfrac{6 + 2\sqrt{5}}{2} \\ \\ \\ x' = {3 + \sqrt{5}} \\ \\ \\ x'' = \dfrac{6 - 2\sqrt{5}}{2} \\ \\ \\ x'' = 3 - \sqrt{5}}$


S = { ${3 + \sqrt{5}} , \ \ {3 - \sqrt{5}}$}

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Soma das raízes x'  +  x''

${3 + \sqrt{5}} \ \ +\ \ {3 - \sqrt{5}} \\ \\ \\ 3 + 3 = 6$

Soma = 6