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January 16, 2017
Posted by **Raj** on Tuesday, June 12, 2012 at 11:15pm.

1. 36x^2+18x+K

2. 3x^2 - 16x+K

- Math -
**Reiny**, Wednesday, June 13, 2012 at 8:39amlet's look at the discriminant.

if b^2 - 4ac is a perfect square, then it can be factored over the rationals, so we start with that.

I will do the 2nd, since it has smaller numbers

for 3x^2 - 16x + k

b^2 - 4ac

= 256-12k

= 4(64-3k)

remember we have to take the square root of that

√(4(64-3k))

= 2√(64-3k)

For 64-3k to be a perfect square

we need 3k to be 0,15,28,39,48,55,60 or 63

of those only 0,15,39,48,60, and 63 are multiples of 3

So for rationals, k could be 0, 5, 13, 16, 20 or 21

testing:

let's try k = 13

3x^2 - 16x + 13

x = (-16 ± √100)/6

= -1 or 13/3

so 3x^2 - 16x + 13 = (x+1)(3x-13)

k = 0, 5, 13, 16, 20, or 21