Question

wyznacz pierwiastki równania :

a) (x+3)(x-1)=0

b) (x-1/2) (x+4)=0

c) (x+7)(x+10)=0

d) (x+2)^2=0

e) (1/3-x) (x-1/4)=0

Answer 1

a) -3, 1

b) 1/2, -4

c) -7, - 10

d) -2

e) 1/3, 1/4

Answer 2

a. (x+3)(x-1)=0

x^2-x+3x-3=0

x^2+2x-3=0

a=1 b=2 c=-3

delta=b^2-4ac

delta=4-4*1*(-3)

delta=4-4*(-3)

delta=4+12

delta=16

x1=-3

x2=1

b.(x-1/2)(x+4)=0

x^2+4x-1/2x-2=0

x^2+3i1/2x-2=0

a=1 b=3i1/2 c=-2

delta=49/4+8

delta=81/4

x1=-2

x2=4

c.(x+7)(x+10)=0

x^2+10x+7x+70=0

x^2+17x+70=0

a=1 b=17 c=70

delta=289-280

delta=9

x1=-13

x2=-4

d.(x+2)^2=0

(x+2)(x+2)=0

x^+2x+2x+4=0

x^2+4x+4=0

a=1 b=4 c=4

delta=16-16

delta=0

x0=-2

e.(1/3-x)(x-1/4)=0

1/3x-1/12-x^2+1/4x=0

-x^2+7/12x-1/12=0

a=-1 b=7/12 c=-1/12

delta=49/144-1/3

delta=49/144-48/144

delta=1

x1=19/24

x2=-5/24