Question

In the equation, t is a constant. If the equation has no real solutions, what could be the value of t? 2x^2 − 4x = t please help im struggling and my teacher doesnt teach me anything sooo

Answer 1

2x^2-4x=t

2x(x-2)=t

if t=0:

0=2x(x-2)

$\frac{0}{2(x - 2)} = x$

so, x=0

if t is not=0:

$x = \frac{t}{2(x - 2)}$

Answer 2

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