Sunday

April 20, 2014

April 20, 2014

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

**Related Questions**

SAT Math - Can I please get some help on these questions: 1. If , find the value...

calc - analyze the function ln x = cx^2 to find the unique value of c such that ...

Math (Absolute Value Inequality) - Find the maximum value of a such that the ...

Math (Absolute Value Inequality) - Find the maximum value of a such that the ...

Calculus AB - Analyze the function ln x=cx^2 to find the unique value of c such...

Calculus - Sorry... Consider the function f(x) = 8.5 x − cos(x) + 2 on the...

Calc III - Hello, Can somebody help me with the following two problems? 1. Find ...

Physics - A uniform electric field of magnitude 75 n/c is created at an angle of...

physics - A uniform electric field of magnitude 75 n/c is created at an angle of...

Math - Given that f(x) = 2sinx - cosx - Write f(x) in the form Asin(x+a) - Find ...