Question

Majca w załączniku ( proste ) pliss;*

Answer 1

Zad.1)a)

2x² -9x -35 = 0

Δ = (-9)² -4*2*(-35) = 81 +280 = 361

√Δ =√361 = 19

x1 = (9 -19):(2*2) = (-10): 4 = -5/2

x2 = ((9 +19):(2*2) = 28:4 =7

 

b)

4x² -13x +3 = 0

Δ = (-13)² -4*4*3 = 169 -48=121

√Δ = √121 =11

x1 = (13-11):(2*4) = 2 : 8 = 1/4

x2 = (13+11):(2*4) = 24 : 8 = 3

 

c)

-6x² +13x +5 = 0

Δ = 13² -4*(-6)*5 = 169 + 120 = 289

√Δ=√289 = 17

x1 = (-13-17):([2*(-6)] = (-30): (-12) = 5/2

x2 = (-13+17):([2*(-6)] = 4: (-12) = - 1/3

 

d)

5x² -6x +6 = 0

Δ = (-6)² -4*5*6 = 36 -120 =  -84

Δ < 0, wiec brak pierwistków równania

 

e)

-2x² +5x -3 = 0

Δ = 5²- 4*(-2)*(-3) = 25 -24 = 1

√Δ= √1 =1

x1 = (-5 -1) : 2(-2)= (-6):(-4) = 3/2

x2 = (-5+1):2*(-2) = (-4) : (-4) = 1

 

f)

4x² +12x +9 = 0

Δ= 12² -4*4*9 = 144 -144 = 0

x1 = x2 = (-12): (2*4) = (-12): 8 = -3/2

 

Zad.2

a)

2x² +3 = -7x

2x² +7x +3 = 0

Δ = 7² -4*2*3 = 49 - 24 = 25

√Δ=√25 = 5

x1 = (-7 -5): (2*2) = (-12): 4 = -3

x2 = (-7 +5):(2*2) = (-2): 4 = -1/2

 

b)

x +10 = 3x²

-3x² +x +10 = 0

Δ = 1² -4*(-3)*10 = 1 +120 =121

√Δ = √121=11

x1= (-1-11):[2*(-3)] = (-12):(-6) = 2

x2 =(-1+11):[2*(-3)] = 10:(-6 ) = -5/3

 

c)

16x² +24√2x  = -18

16x² +24√2 x +18 = 0       /:2

8x² +12√2x +9 = 0

Δ = (12√2)² - 4*8*9 = 144*2 - 288 = 288 -288 = 0

x1 = x2 = (-12√2): (2*8) = (-12√2): 16 = -¾√2

 

d)

-2x -3x² +6 = 0

-3x² -2x +6 = 0

Δ = (-2)² -4*(-3)*6 = 4 + 72 = 76

√Δ = √76 = √4*√19 = 2√19

x1 = (2 -2√19) :[2*(-3) ]= 2(1 - √19):(-6) = -⅓*(1- √19)

x2 =(2 +2√19) :[2*(-3) ]= 2(1 + √19):(-6) = -⅓*(1-+ √19)

 

e)

5x² = 2 -2x

5x² +2x -2 = 0

Δ = 2² - 4*5*(-2) = 4 + 80 = 84

√Δ= √84 = √4*√21 = 2√21

x1 = (-2 - 2√21) : (2*5) = -2(1 +√21) : 10 =( -1/5)*(1 +√21)

x2 = (-2 + 2√21) : (2*5) = -2(1 -√21) : 10 =( -1/5)*(1 +√21)

 

f)

5x² = 8x -5

5x² -8x +5 = 0

Δ = (-8)² -4*5*5 = 64 -100 = - 36

Δ < 0, więc brak jest pierwiastków równania