Question

Resolva as equações de 2° grau a seguir:

$a) \: 4 {y}^{2} - 100 = 0$
$b) \: 3 {x}^{2} - x = 0$
$c) \: 4 {x}^{2} - 25 = 0$
$d) \: 4 {x}^{2} - 5x = 0$

Answer 1

Bom Dia

a)

$4y {}^{2} - 100 = 0$

$4y {}^{2} = 100$

$y {}^{2} = 25$

$y = \frac{ + }{ - } 5$

$y = 5$

$y = - 5$

R: $y_{1} = - 5.y_{2} = 5$

b)

$3x {}^{2} - x = 0$

$x \times (3x - 1) = 0$

$x = 0$

$3x - 1 = 0$

$x = \frac{1}{3}$

R: $x_{1} = 0.x_{2} = \frac{1}{3}$

c)

$4x {}^{2} - 25 = 0$

$4x {}^{2} = 25$

$x {}^{2} = \frac{25}{4}$

$x = \frac{ + }{ - } \frac{5}{2}$

$x = \frac{5}{2}$

$x = - \frac{5}{2}$

R: $x_{1} = - \frac{5}{2} .x_{2} = \frac{5}{2}$

d)

$4x {}^{2} - 5x = 0$

$x \times (4x - 5) = 0$

$x = 0$

$4x - 5 = 0$

$x = 0$

$x = \frac{5}{4}$

R: $x_{1} = 0.x_{2} = \frac{5}{4}$


Espero ter ajudado e bons estudos :)