Question

Considere a função a baixo,e faça o que se pede:
$y = - 3 x {}^{2} + 30x - 72$
a)identifique os coeficientes a,b e c:

b)Calcule o discriminante (delta)=b2-4.a.c :

c)determine o valor de x1 e x2​

Answer 1

Explicação passo-a-passo:

a) $\sf y=-3x^2+30x-72$

$\sf y=ax^2+bx+c$

$\sf a=-3,~b=30,~c=-72$

b) $\sf \Delta=b^2-4\cdot a\cdot c$

$\sf \Delta=30^2-4\cdot(-3)\cdot(-72)$

$\sf \Delta=900-864$

$\sf \Delta=36$

c) $\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}$

$\sf x=\dfrac{-30\pm\sqrt{36}}{2\cdot(-3)}$

$\sf x=\dfrac{-30\pm6}{-6}$

• $\sf x_1=\dfrac{-30+6}{-6}~\longrightarrow~x_1=\dfrac{-24}{-6}~\longrightarrow~x_1=4$

• $\sf x_2=\dfrac{-30-6}{-6}~\longrightarrow~x_2=\dfrac{-36}{-6}~\longrightarrow~x_2=6$

$\sf S=\{4,6\}$