Question

PROSZĘ O PILNĄ POMOC! SZYBKO NA ZARAZ!

Answer 1

A)x²+4x-21=0 
Δ= b² - 4ac = 4² - 4*1*(-21) =16 + 84 =100
√Δ = √100 = 10
x₁ = (-b-√Δ)/2a = (-4-10)/2 = -14/2 = -7
x₂ = (-b+√Δ)/2a = (-4+10)/2 =6/2  = 3

b)6-x-x²=0-x² -x +6 = 0
Δ= b² - 4ac = (-1)² - 4*(-1)*6 = 1 +24 =25
√Δ = √25 = 5
x₁ = (-b-√Δ)/2a = (1-5)/-2 = -4/-2 = 2
x₂ = (-b+√Δ)/2a = (1+5)/-2 = 6/-2 = -3 

c)x-x²+12=0-x² +x+12=0
Δ= b² - 4ac = 1² - 4*(-1)*12 = 1 +24 =25
√Δ = √25=5
x₁ = (-b-√Δ)/2a = (-1-5)/-2 = -6/-2 = 3
x₂ = (-b+√Δ)/2a = (-1+5)/-2 = 4/-2 = -2

d)2x²+5x-3=0
Δ= b² - 4ac = 5² - 4*2*(-3) = 25 + 24=49
√Δ = √49 = 7
x₁ = (-b-√Δ)/2a = (-5-7)/4 = -12/4 =  - 3
x₂ = (-b+√Δ)/2a = (-5+7)/4 =  2/4 = 1/2

e)-6x²-7x+5=0
Δ= b² - 4ac = (-7)² - 4*(-6)*5 = 49 +120 =169
√Δ = √169 = 13
x₁ = (-b-√Δ)/2a = (7 -13)/-12 = -6/-12 = ½
x₂ = (-b+√Δ)/2a = (7 +13)/-12 = 20/-12 = -5/3 = - 2 i 2/3

f)9/4x²-12x+16=0   I*4
9x² -48x + 64 = 0
Δ= b² - 4ac = (-48)² - 4*9*64 = 2304 – 2304=0
x⁰ = -b/2a = 48/18 = 8/3 = 2 i 2/3

g)2x²-3x-1=0
Δ= b² - 4ac =(-3)² - 4*2*(-1) = 9 +8=17
√Δ = √17
x₁ = (-b-√Δ)/2a = (3-√17)/4
x₂ = (-b+√Δ)/2a = (3+√17)/4

h)3x²+5x+1=0
Δ= b² - 4ac = 5² - 4*3*1 = 25 -12 = 13
√Δ = √13
x₁ = (-b-√Δ)/2a = (-5-√13)/6
x₂ = (-b+√Δ)/2a = (-5+√13)/6

i)-x²+³√2x-5=0
Δ= b² - 4ac =(³√2)² - 4*(-1)*(-5) = 2√2 – 20 = 2* 1,41 – 20 = 2,82-20 = -17,19
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