Question

What's are the zeros for x squared - 13x + 67

Answer 1

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

`x= (-b+/- √(b^2-4ac) )/(2a)`
given
0=1x²-13+67
a=1
b=-13
c=67

note: √-1=i

`x= (-(-13)+/- √((-13)^2-4(1)(67)) )/(2(1))`

`x= (13+/- √(169-268) )/(2)`

`x= (13+/- √(-99) )/(2)`

`x= (13+/- (√(-1))(√(9))(√(11)) )/(2)`

`x= (13+/- (i)(3)(√(11)) )/(2)`

`x= (13+/- 3i√(11) )/(2)`

there are actually no real zeroes of the function

Answer 2

There are no real solutions or zero for this equation as the discriminant is less than 0.

(b^2-4ac)=-99, there is no real square root of -99 so there are no real solutions.