Jawaban:

2a.

2x²+3x+1=0

(2x+1)(x+1) = 0

x1 = -½

x2 = -1

2b.

-6x²-x+15=0

(-2x+3)(3x+5) = 0

x1 = 3/2

x2 = -5/3

3a.

x²+3x-18=0 ==> a=1 b=3 c=-18

x1•x2 = c/a

= -18/1

= -18

b.

x1+x2 = -b/a

= - 3/1

= -3

4.

jika akar2 lamanya x1 & x2, maka akar2 barunya 3x1 & 3x2

persamaan:

(x - 3x1)(x - 3x2) = 0

x² - 3x1•x - 3x2•x + 9x1•x2 = 0

x² - 3x(x1 - x2) + 9(x1•x2) = 0

x² - 3x(-b/a) + 9(c/a) = 0

x² - 3x(-5) + 9(6) = 0

x² + 15x + 54 = 0

5.

mis: y = ax²+bx+c ==> masuk'in aja nilai x & y

persamaan 1:

13 = a(-2)²+b(-2)+c

13 = 4a-2b+c

persamaan 2:

4 = a(1)²+b(1)+c

4 = a+b+c

persamaan 3:

8 = a(3)²+b(3)+c

8 = 9a+3b+c

1&2:

13 = 4a-2b+c

4 = a+b+c

-------------------- (-)

9 = 3a-3b

3 = a-b --> persamaan 4

2&3:

8 = 9a+3b+c

4 = a+b+c

------------------- (-)

4 = 8a+2b

2 = 4a+b --> persamaan 5

4&5:

3 = a-b

2 = 4a+b

------------------- (+)

5 = 5a

a = 1

b = -2

c = 5

persamaan: x²-2x+5=0