Question

ME AJUDEM POR FAVOR

Encontre o descriminante (Delta) da equação a equação do segundo grau -3x² – 4x +7 = 0

Answer 1

Resposta:

$-3x^2-4x+7=0\\\\\mathrm{Para\:uma\:equacao\:de\:segundo\:grau\:da\:forma\:}ax^2+bx+c=0\mathrm{\:as\:solucoes\:sao\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{Para\:}\quad a=-3,\:b=-4,\:c=7\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\left(-3\right)\cdot \:7}}{2\left(-3\right)}\\\\\sqrt{\left(-4\right)^2-4\left(-3\right)\cdot \:7}\\\\Aplicar \ regra \ -(-a)=a\\\\=\sqrt{\left(-4\right)^2+4\cdot \:3\cdot \:7}\\\\\left(-4\right)^2=4^2$

$=\sqrt{4^2+4\cdot \:3\cdot \:7}\\\\\mathrm{Multiplicar\:os\:numeros:}\:4\cdot \:3\cdot \:7=84\\\\=\sqrt{4^2+84}\\\\4^2=16\\\\=\sqrt{16+84}\\\\\mathrm{Somar:}\:16+84=100\\\\=\sqrt{100}\\\\\mathrm{Fatorar\:o\:numero:\:}\:100=10^2\\\\=\sqrt{10^2}\\\\\sqrt[n]{a^n}=a\\\\\sqrt{10^2}=10\\\\=10\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \:10}{2\left(-3\right)}$

$x_1=\frac{-\left(-4\right)+10}{2\left(-3\right)},\:x_2=\frac{-\left(-4\right)-10}{2\left(-3\right)}\\\\\frac{-\left(-4\right)+10}{2\left(-3\right)}\\\\=\frac{4+10}{-2\cdot \:3}\\\\\mathrm{Somar:}\:4+10=14\\\\=\frac{14}{-2\cdot \:3}\\\\\mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:3=6\\\\=\frac{14}{-6}\\\\\frac{a}{-b}=-\frac{a}{b}\\\\=-\frac{14}{6}\\\\\mathrm{Eliminar\:o\:fator\:comum:}\:2\\\\=-\frac{7}{3}$

$\frac{-\left(-4\right)-10}{2\left(-3\right)}\\\\=\frac{4-10}{-2\cdot \:3}\\\\\mathrm{Subtrair:}\:4-10=-6\\\\=\frac{-6}{-2\cdot \:3}\\\\\mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:3=6\\\\=\frac{-6}{-6}\\\\=\frac{6}{6}\\\\\mathrm{Aplicar\:a\:regra}\:\frac{a}{a}=1\\\\=1\\\\\mathrm{As\:solucoes\:para\:a\:equacao\:de\:segundo\:grau\:sao:\:}\\\\x=-\frac{7}{3}\\\\\:x=1$

Answer 2

$\large \boxed{ \begin{array}{l}\Delta = b {}^{2} - 4ac \\ \Delta = ( - 4) {}^{2} - 4 \cdot( - 3) \cdot7 \\ \Delta = 16 + 84 \\ \Delta = 100 \end{array}}$