Utilizando o processo algébrico de bhaskara, determine as raiz...
Utilizando o processo algébrico de bhaskara, determine as raizes das equações do 2º grau no conjunto dos números reais :a)x²+2x-3=0
b)x²+10x+25=0
c)3x²-2x-1=0
d)10x²+7x+1=0
b)x²+10x+25=0
c)3x²-2x-1=0
d)10x²+7x+1=0
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![x = frac{-b pm sqrt{b^2 -4*a*c}}{2*a}]()
![a) \ x^2 - 10x + 9 = 0]()
a=1, b=−10, c=9
Δ=b2−4ac
Δ=(−10)2−4*(1)*(9)
Δ=100−36
Δ=64
![\ \ x = frac{-b pm sqrt{ riangle}}{2*a} \ \ x = frac{-(-10) pm sqrt{64}}{2*1} \ \ x = frac{10 pm 8}{2} \ \ x' = frac{10 + 8}{2} \ \ x' = frac{18}{2} \ \ x' = 9 \ \ x'' = frac{10 - 8}{2} \ \ x'' = frac{2}{2} \ \ x'' = 1]()
S = {9, 1}
=======================================
![b)\x^2 + x - 6 = 0]()
a=1, b=1, c=−6
Δ=b2−4ac
Δ=(1)2−4*(1)*(−6)
Δ=1+24
Δ=25
![x = frac{-b pm sqrt{ riangle}}{2*a}\ \x = frac{-1 pm sqrt{25}}{2*1}\ \x = frac{-1 pm 5}{2} \ \ x' = frac{-1 + 5}{2}\ \x' = frac{4}{2}\ \x' = 2\ \ \x'' = frac{-1 - 5}{2}\ \x'' = frac{-6}{2}\ \x'' = -3]()
S = {2, -3}
=======================================
![c)\x^2 + 4x - 5 = 0]()
![x = frac{-b pm sqrt{ riangle}}{2*a}]()
a=1, b=4, c=−5
Δ=b2−4ac
Δ=(4)2−4*(1)*(−5)
Δ=16+20
Δ=36
![x = frac{-4 pm sqrt{36}}{2*1}\ \x = frac{-4 pm 6}{2}\ \x' = frac{-4 + 6}{2}\ \ x' = frac{2}{2}\ \x' = 1\ \ \x'' = frac{-4 - 6}{2}\ \x'' = frac{-10}{2}\ \x'' = -5]()
S = {1, -5}
=======================================
![d)x^2-10x + 24 = 0]()
a=1, b=−10, c=24
Δ=b2−4ac
Δ=(−10)2−4*(1)*(24)
Δ=100−96
Δ=4
![x = frac{-b pm sqrt{ riangle}}{2*a}]()
![x = frac{-(-10) pm sqrt{4}}{2*1}\ \x = frac{10 pm 2}{2}\ \ x' = frac{10 + 2}{2}\ \x' = frac{12}{2}\ \x' = 6\ \ \ x'' = frac{10 - 2}{2}\ \ x'' = frac{8}{2}\ \x'' = 4]()
S = {6, 4}
=======================================
![e)\2x^2-9x+4 = 0]()
a=2, b=−9, c=4
Δ=b2−4ac
Δ=(−9)2−4*(2)*(4)
Δ=81−32
Δ=49
![x = frac{-b pm sqrt{ riangle}}{2*a}\ \x = frac{-(-9) pm sqrt{49}}{2*2}\ \x = frac{9 pm 7}{4}\ \x' = frac{9 + 7}{4}\ \x' = frac{16}{4}\ \x' = 4\ \ \x'' = frac{9 + 7}{4}\ \x'' = frac{2}{4}\ \x'' = frac{1}{2}]()
S = {4,![frac{1}{2}]()
}
=======================================
![f)\x^2+8x+16 = 0]()
a=1, b=8, c=16
Δ=b2−4ac
Δ=(8)2−4*(1)*(16)
Δ=64−64
Δ=0
![x = frac{-b pm sqrt{ riangle}}{2*a}\ \x = frac{-8 pm sqrt{0}}{2*1}\ \x = frac{-8 pm 0}{2*1}\ \x' = frac{-8 + 0}{2}\ \x ' = -4\ \x'' = frac{-8 - 0}{2}\ \x''= -4]()
S = {-4}
a=1, b=−10, c=9
Δ=b2−4ac
Δ=(−10)2−4*(1)*(9)
Δ=100−36
Δ=64
S = {9, 1}
=======================================
a=1, b=1, c=−6
Δ=b2−4ac
Δ=(1)2−4*(1)*(−6)
Δ=1+24
Δ=25
S = {2, -3}
=======================================
a=1, b=4, c=−5
Δ=b2−4ac
Δ=(4)2−4*(1)*(−5)
Δ=16+20
Δ=36
S = {1, -5}
=======================================
a=1, b=−10, c=24
Δ=b2−4ac
Δ=(−10)2−4*(1)*(24)
Δ=100−96
Δ=4
S = {6, 4}
=======================================
a=2, b=−9, c=4
Δ=b2−4ac
Δ=(−9)2−4*(2)*(4)
Δ=81−32
Δ=49
S = {4,
}=======================================
a=1, b=8, c=16
Δ=b2−4ac
Δ=(8)2−4*(1)*(16)
Δ=64−64
Δ=0
S = {-4}
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