Question

Com a formula de Bhaskara, resolva as seguintes equações:

a) 2x² + 7x + 5 = 0

b) x² + 5x - 14 = 0

c) x² - 6x + 9 = 0

Com o calculo completo se possível, grata.

Answer 1

a) 2x² + 7x + 5 = 0 
Delta = b² - 4ac
Delta = 49 - 4(2)(5)
Delta = 49 - 40
Delta = 9

X = (-b +- raiz delta) / 2a
X = (-7 +- 3) / 4
x' = (-7 + 3) / 4 = -4/4 = -1
x" = (-7 - 3) / 4 = -10/4 = -5/2

b) x² + 5x - 14 = 0 
Delta = b² - 4ac
Delta = 25 - 4(1)(-14)
Delta = 25 + 56
Delta = 81

X = (-b +- raiz delta) / 2a
X = (-5 +- 9) / 2
x' = (-5 + 9) / 2 = 4/2 = 2
x" = (-5 - 9) / 2 = -14/2 = -7

c) x² - 6x + 9 = 0 
Delta = b² - 4ac
Delta = 36 - 4(1)(9)
Delta = 36 - 36
Delta = 0

X = (-b +- raiz delta) / 2a
X = (6 +- 0) / 2
x' = (6 + 0) / 2 = 6/2 = 3
x" = (6 - 0) / 2 = 6/2 = 3

Answer 2

a) Δ = 7² - 4 x 2 x 5
Δ= 49- 40
Δ= 9

x=$\frac{-7+- \sqrt{9} }{4}$ = 
x1 = $\frac{-7+3}{4}$ = -1
x2= $\frac{-7-3}{4}$= -2,5

b) Δ= 25 - 4 x 1 x (-14)
Δ= 25+56
Δ= 81

x=$\frac{-5+- \sqrt{81} }{2}$=
x1= $\frac{-5+9}{2}$= 2
x2= $\frac{-5-9}{2}$= -7

c)Δ= 36 - 4 x 1 x 9
Δ=0

x= $\frac{-(-6)+- \sqrt{0} }{2}$=
x= $\frac{6}{2}$= 3