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

Answer 1

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

\]

Answer 2

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

Answer 3

exactly one solution

Answer 4

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) \\

\]