Question

Equação do 2 grau, formula de bhaskara.

A-) X²-8X=-15
B-) X²-3X+2=0
C-) 2X²-21X+60=0

Answer 1

a)
$X^2-8X=-15 => x^2 - 8x +15 = 0$

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

Vamos encontrar o delta (Δ)
Δ=b2−4ac
Δ=(−8)2−4*(1)*(15)
Δ=64−60
Δ=4

$x = \frac{-b \pm \sqrt{\triangle}}{2*a} \\ \\ x = \frac{-(-8) \pm \sqrt{4}}{2*1} \\ \\ x = \frac{8 \pm \sqrt{4}}{2} \\ \\ x = \frac{8 \pm 2}{2} \\ \\ \\ x' = \frac{8 + 2}{2} \\ \\ x' = \frac{10}{2} \\ \\ x' = 5 \\ \\ \\ x'' = \frac{8 - 2}{2} \\ \\ x'' = \frac{6}{2} \\ \\ x'' = 3$

S = {5, 3}

b) 
$X^2-3X+2=0$

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

Vamos encontrar o delta (Δ)

Δ=b2−4ac
Δ=(−3)2−4*(1)*(2)
Δ=9−8
Δ=1

$x = \frac{-b \pm \sqrt{\triangle}}{2*a} \\ \\ \\ x = \frac{-(-3) \pm \sqrt{1}}{2*1} \\ \\ x = \frac{3 \pm \sqrt{1}}{2} \\ \\ x = \frac{3 \pm 1}{2} \\ \\ x' = \frac{3 + 1}{2} \\ \\ x' = \frac{4}{2} \\ \\ x' = 2 \\ \\ \\ x'' = \frac{3 - 1}{2} \\ \\ x'' = \frac{2}{2} \\ \\ x'' = 1$

S = {2, 1}

c) 

$2x^2-21x+60=0$

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

Vamos encontrar o delta (Δ)

Δ=b2−4ac
Δ=(−21)2−4*(2)*(60)
Δ=441−480
Δ=−39

Como Δ < 0, não existem raízes para o conjunto de R