Answer:
Discriminant is -20 (D<0, no real roots)
Step-by-step explanation:
The Discriminant Formula:
[tex] \displaystyle \large{ D = {b}^{2} - 4ac}[/tex]
First, arrange expression in the standard form or ax^2+bx+c = 0.
[tex] \displaystyle \large{ {x}^{2} - 4x = 9} \\ \displaystyle \large{ {x}^{2} - 4x - 9 = 0}[/tex]
From above, we subtract both sides by 9.
Compare the coefficients:
[tex] \displaystyle \large{a {x}^{2} + bx + c = {x}^{2} - 4x - 9}[/tex]
Substitute a = 1, b = -4 and c = -9 in the formula.
[tex] \displaystyle \large{ D = {( - 4)}^{2} - 4(1)( - 9)} \\ \displaystyle \large{ D = 16 - 4( - 9)} \\ \displaystyle \large{ D = 16 - 36} \\ \displaystyle \large{ D = - 20}[/tex]
Therefore the discriminant of equation is -20 which is less than 0.
