. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x2 = 3x – 6

Question

. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x2 = 3x – 6

anonymous · Answer

$$ x^2 - 3 x +6 =0\
a x^2 + b x + c=0\
\Delta = b^2 - 4 a c 

$$

anonymous · Answer

$$\Delta = (-3)^2 - 4(1)(6)= 9 - 24= -15
$$
What can you conclude?

anonymous · Answer

exactly one solution

anonymous · Answer

No.
No real roots. Two complex roots
$$

 x=\frac{1}{2} \left(3-i
   \sqrt{15}\right) \
 x=\frac{1}{2} \left(3+i
   \sqrt{15}\right) \

$$