zeroes are where the function equals 0 so
solve
0=x²-13x+67
factor
what 2 numbres multiply to get 67 and add to get -13?
nothing
so we use quadratic formula
for
0=ax²+bx+c
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
given
0=1x²-13+67
a=1
b=-13
c=67
note: √-1=i
[tex]x= \frac{-(-13)+/- \sqrt{(-13)^2-4(1)(67)} }{2(1)} [/tex]
[tex]x= \frac{13+/- \sqrt{169-268} }{2} [/tex]
[tex]x= \frac{13+/- \sqrt{-99} }{2} [/tex]
[tex]x= \frac{13+/- (\sqrt{-1})(\sqrt{9})(\sqrt{11}) }{2} [/tex]
[tex]x= \frac{13+/- (i)(3)(\sqrt{11}) }{2} [/tex]
[tex]x= \frac{13+/- 3i\sqrt{11} }{2} [/tex]
there are actually no real zeroes of the function
