Find the values of P (1 Viewer)

[blacktown_]

Find the values of P for which x^2-x+3p-2>0 for all x

 

[Carrotsticks]

For this to occur, the minimum point must be above the y axis

The minimum point occurs at x=1/2 and subbing that in, we have y=-3/4 + 3p-2 = 3p-11/4

But this has to be greater than 0, so 3p-11/4 > 0. Solving his, we have p > 11/12.

Alternatively, you could let the discriminant be less than than zero, since we already know that it's a positive quadratic.

 

[twinklegal19]

For this to occur, the minimum point must be above the y axis

The minimum point occurs at x=1/2 and subbing that in, we have y=-3/4 + 3p-2 = 3p-11/4

But this has to be greater than 0, so 3p-11/4 > 0. Solving his, we have p > 11/12.

Alternatively, you could let the discriminant be greater than zero, since we already know that it's a positive quadratic.

Less than*

 

[4025808]

Less than*

Nice work

 

[Carrotsticks]

Less than*

Yep that's right, I have fixed my answer =)

 

[blacktown_]

thanks