Maths Methods - Unit 1 help.

[Scrono13]

Hey, I really need help with how to finish off my answers with the following;
For what values of k does the equation 2kx^2-3x+k=0 have: one solution, 2 solutions and 0 solutions.

Thanks

[Phy124]

Hey, I really need help with how to finish off my answers with the following;
For what values of k does the equation 2kx^2-3x+k=0 have: one solution, 2 solutions and 0 solutions.

Thanks

For any quadratic the discriminant is given by

A quadratic will have 2 solutions when , 1 solution when and no solutions when

Spoiler

for 2 solutions:





For 1 solution:





For no solutions:





If you're struggling getting the solutions from the initial equation try graphing the function and noting the intercepts, then note the x values for which the function is greater y, less than y and equal to y.

edit: thanks to Polonius for noting a missing 8

[Scrono13]

Thanks a lot

[Professor Polonsky]

Shouldn't there be an 8 there?

[Phy124]

Shouldn't there be an 8 there?

Nothing to see here folks 

[Scrono13]

How do I write the following in interval notation?

R+\{2<x<6}

and

R+∪{-2<x≤0}

Thanks!

By the wa

[Professor Polonsky]

The first one includes all positive reals, excluding numbers between 2 and 6 (2<x<6). So you're going to have two different intervals here.

Spoiler

The second one again includes all positive reals, but this time including numbers between -2 and 0 (inclusive of the latter).

Spoiler

[Scrono13]

Can I ask, why are they square brackets when 2 and 6 aren't included?

[Professor Polonsky]

2 and 6 are not included as part of the complement (the excluded bits). Therefore, they are included.

[Scrono13]

Got it, thanks