Question

6- Encontre o valor de f(x) = x² + 3x – 10 para que f(x) = 0 * 5 pontos

Answer 1

Resposta:

Explicação passo-a-passo:

Para f(x)=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+3x-10=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=3~e~c=-10\\\\\Delta=(b)^{2}-4(a)(c)=(3)^{2}-4(1)(-10)=9-(-40)=49\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(3)-\sqrt{49}}{2(1)}=\frac{-3-7}{2}=\frac{-10}{2}=-5\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(3)+\sqrt{49}}{2(1)}=\frac{-3+7}{2}=\frac{4}{2}=2\\\\S=\{-5,~2\}$

Answer 2

Explicação passo-a-passo:

$f(x)=x^2+3x-10$

$f(x)=0$

$x^2+3x-10=0$

$\Delta=3^2-4\cdot1\cdot(-10)$

$\Delta=9+40$

$\Delta=49$

$x=\dfrac{-3\pm\sqrt{49}}{2\cdot1}$

$x=\dfrac{-3\pm7}{2}$

$x'=\dfrac{-3+7}{2}~\Rightarrow~\boxed{x'=2}$

$x"=\dfrac{-3-7}{2}~\Rightarrow~\boxed{x"=-5}$