2x^2-4x=t
2x(x-2)=t
if t=0:
0=2x(x-2)
[tex] \frac{0}{2(x - 2)} = x[/tex]
so, x=0
if t is not=0:
[tex]x = \frac{t}{2(x - 2)} [/tex]
Answer:
t>-2
Step-by-step explanation:
Given a quadratic equation ax²+bx+c = 0, the solutions to the equal can either be real or no real solution (complex).
For the equation to have a complex solution, the discriminant given as D = b²-4ac must be greater than zero i.e
b²-4ac > 0
Given the quadratic equation:
2x² − 4x = t
It can also be written as:
2x²-4x-t = 0
Where a = 2, b = -4 and c= -t
For the equation to have no real solution, b²-4ac > 0
(-4)² - 4(2)(-t) > 0
16+8t >. 0
16 > -8t
Dividing both sides by -8:
16/-8 < -8t/-8 (the sign change is because we divide both sides of the inequality by a negative value)
-2<t OR t>-2
The value of t will be greater than -2
