Question

prosze o zrobienie tych dwoch zaznaczonych zadan na zdjeciu w zalaczniku, błagam na dzisiaj

Answer 1

Zad. 8

a.) x2 – 3x – 10 > 0            i             1/2x – 1 < 0

delta = b2 – 4ac = (-3)2 – 4*1*(-10) = 9 + 40 = 49
delta z pierwiastka z 49 = 7

x1 = -b – pierwiastek z delty/2a = 3 – 7/2*1 = -4/2 = -2

x2 = -b + pierwiastek z delty/2a = 3 + 7/2*1 = 10/2 = 5

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1/2x – 1 < 0
1/2x < 1 /: (1/2)

x < 2

 

b.) -2x2 + 13x – 15 < 0           i          3/2x – 9 >równe 0

delta = b2 – 4ac = (13)2 – 4*(-2)*(-15) = 169 – 120 = 49

delta z pierwiastka z 49 = 7

x1 = -b – pierwiastek z delty/2a = -13 – 7/2*(-2) = -20/-4 = 5

x1 = -b + pierwiastek z delty/2a = -13 + 7/2*(-2) = - 6/-4 = 3/2

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3/2x – 9 >równe 0

3/2x >równe 9/: (3/2)

x >równe 6

 

 

c.) x2 + 9x + 14 >równe 0          i               x2 – 2x >równe 15

delta = b2 – 4ac = (9)2 – 4*1*14 = 81 – 56 = 25

delta z pierwiastka z 25 = 5

x1 = -b – pierwiastek z delty/2a = -9 – 5/2*1 = -14/2 = -7

x1 = -b + pierwiastek z delty/2a = -9 + 5/2*1 = -4/2 = -2

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x2 – 2x >równe 15

x2 – 2x - 15 >równe 0

delta = b2 – 4ac = (-2)2 – 4*1*(-15) = 4 + 60 = 64

delta z pierwiastka z 64 = 8

x1 = -b – pierwiastek z delty/2a = 2 – 8/2*1 = -6/2 = -3

x1 = -b + pierwiastek z delty/2a = 2 + 8/2*1 = 10/2 = 5

 

d.) 2x2 + 17x + 30 >równe 0      i     1/2x2 - 4x < 8

delta = b2 – 4ac = (17)2 – 4*2*30 = 289 – 240 = 49

delta z pierwiastka z 49 = 7

x1 = -b – pierwiastek z delty/2a = -17 – 7/2*2 = -24/4 = -6

x2 = -b + pierwiastek z delty/2a = -17 + 7/2*2 = -10/2 = -5

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1/2x2 - 4x < 8

1/2x2 - 4x – 8 < 0

delta = b2 – 4ac = (-4)2 – 4*(1/2)*(-8) = 16 + 16 = 32

delta z pierwiastka z 32 = 2 pierwiastek 2

x1 = -b – pierwiastek z delty/2a = 4 - 2 pierwiastek 2/2*(1/2) = 4 - 2 pierwiastek 2/1 = 4 - 2 pierwiastek 2

x2 = -b + pierwiastek z delty/2a = 4 + 2 pierwiastek 2/2*(1/2) = 4 + 2 pierwiastek 2/1 = 4 + 2 pierwiastek 2