Question

BHASKARA!!! (AJUDA)

A) -2x^2+2x+12=0

B) 4x^2-2x-6=0

C) x^2-x-25=0

D) 9x^2+2x+4=0

E) x^2+4x+1=0

Answer 1

Boa noite!

a)
$-2x^2+2x+12=0\text{ dividindo por -2}\\ x^2-x-6=0\\ \Delta=(-1)^2-4(1)(-6)=1+24=25\\ x=\frac{-(-1)\pm\sqrt{25}}{2(1)}\\ x=\frac{1\pm{5}}{2}\\ x'=\frac{1+5}{2}=3\\ x''=\frac{1-5}{2}=-2$

b)
$4x^2-2x-6=0\text{ dividindo por 2}\\ 2x^2-x-3=0\\ \Delta=(-1)^2-4(2)(-3)=1+24=25\\ x=\frac{-(-1)\pm\sqrt{25}}{2(2)}\\ x=\frac{1\pm{5}}{4}\\ x'=\frac{1+5}{4}=\frac{3}{2}\\ x''=\frac{1-5}{4}=-1$

c)
$x^2-x-25=0\\ \Delta=(-1)^2-4(1)(-25)=101\\ x=\frac{-(-1)\pm\sqrt{101}}{2(1)}\\ x=\frac{1\pm\sqrt{101}}{2}\\ x'=\frac{1+\sqrt{101}}{2}\\ x''=\frac{1-\sqrt{101}}{2}$

d)
$9x^2+2x+4=0\\ \Delta=(2)^2-4(9)(4)=4-144=-140 \text{Nao ha raizes reais!}$

e)
$x^2+4x+1=0\\ \Delta=(4)^2-4(1)(1)=16-4=12\\ x=\frac{-(4)\pm\sqrt{12}}{2(1)}\\ x=\frac{-4\pm{2}\sqrt{3}}{2}\\ x'=\frac{-4+{2}\sqrt{3}}{2}=-2+\sqrt{3}\\ x''=\frac{-4-{2}\sqrt{3}}{2}=-2-\sqrt{3}$

Espero ter ajudado!

Answer 2

A) -2x² + 2x + 12 = 0

Δ = b² - 4.a.c
Δ = (2)² - 4.(-2).(12)
Δ = 4 + 96
Δ = 100


$x \ = \ \frac{-b \ ^+_- \ \sqrt{\Delta}}{2.a}$

$x \ = \ \frac{-(2) \ ^+_- \ \sqrt{100}}{2.(-2)}$

$x \ = \ \frac{-2 \ ^+_- \ 10}{-4}$



$x' \ = \ \frac{-2 \ + \ 10}{-4}$

$x' \ = \ \frac{8}{-4}$

$x' \ = \ -2$



$x'' \ = \ \frac{-2 \ - \ 10}{-4}$

$x'' \ = \ \frac{-12}{-4}$

$x'' \ = \ 3$


$\boxed{\bold{S \ = \ (-2, \ 3)}}$



B) 4x² - 2x - 6 = 0

Δ = b² - 4.a.c
Δ = (-2)² - 4.(4).(-6)
Δ = 4 + 96
Δ = 100


$x \ = \ \frac{-b \ ^+_- \ \sqrt{\Delta}}{2.a}$

$x \ = \ \frac{-(-2) \ ^+_- \ \sqrt{100}}{2.(4)}$

$x \ = \ \frac{2 \ ^+_- \ 10}{8}$



$x' \ = \ \frac{2 \ + \ 10}{8}$

$x' \ = \ \frac{12}{8}$

$x' \ = \ \frac{3}{2}$



$x'' \ = \ \frac{2 \ - \ 10}{8}$

$x'' \ = \ \frac{-8}{8}$

$x'' \ = \ -1$


$\boxed{\bold{S \ = \ (\frac{3}{2}, \ -1)}}$



C) x² - x - 25 = 0

Δ = b² - 4.a.c
Δ = (-1)² - 4.(1).(-25)
Δ = 1 + 100
Δ = 101


$x \ = \ \frac{-b \ ^+_- \ \sqrt{\Delta}}{2.a}$

$x \ = \ \frac{-(-1) \ ^+_- \ \sqrt{101}}{2.(1)}$

$x \ = \ \frac{1 \ ^+_- \ \sqrt{101}}{2}$


$x' \ = \ \frac{1 \ + \ \sqrt{101}}{2}$


$x'' \ = \ \frac{1 \ - \ \sqrt{101}}{2}$


$\boxed{\bold{S \ = \ (\frac{1 \ + \ \sqrt{101}}{2}, \ \frac{1 \ - \ \sqrt{101}}{2})}}$

 

D) 9x² + 2x + 4 = 0

Δ = b² - 4.a.c
Δ = (2)² - 4.(9).(4)
Δ = 4 - 144
Δ = -140

Não existem raízes reais para esta equação.



E) x² + 4x + 1 = 0

Δ = b² - 4.a.c
Δ = (4)² - 4.(1).(1)
Δ = 16 - 4
Δ = 12


$x \ = \ \frac{-b \ ^+_- \ \sqrt{\Delta}}{2.a}$

$x \ = \ \frac{-(4) \ ^+_- \ \sqrt{12}}{2.(1)}$

$x \ = \ \frac{-4 \ ^+_- \ \sqrt{4 \ . \ 3}}{2}$

$x \ = \ \frac{-4 \ ^+_- \ 2\sqrt{3}}{2}$



$x' \ = \ \frac{-4 \ + \ 2\sqrt{3}}{2}$

$x' \ = \ \frac{-4}{2} \ + \ \frac{2\sqrt{3}}{2}$

$x' \ = \ -2 \ + \ \sqrt{3}$



$x'' \ = \ \frac{-4 \ - \ 2\sqrt{3}}{2}$

$x'' \ = \ \frac{-4}{2} \ - \ \frac{2\sqrt{3}}{2}$

$x'' \ = \ -2 \ - \ \sqrt{3}$


$\boxed{\bold{S \ = \ (-2 \ + \ \sqrt{3}, \ -2 \ - \ \sqrt{3})}}$