Question

Find all values of k for which the trinomial can be factored. a) x^2 +kx - 15 b) 3x^2 - x + k

Answer 1

what times what is -15?

Answer 2

there are multiple answers to what I'm asking

Answer 3

first one -15= 3*-5 and -3*5 now k is the sum of 3 and -5 or sum of -3 and 5 so k is -2 or 2

Answer 4

second one the product is 3k and the sum is -1
so 3+k=-1 implies k=-4

Answer 5

-15 can also be written as -1*15 or 1*(-15) @jango_IN_DTOWN

Answer 6

@freckles oops, yeah then add them.;)

Answer 7

Yes, jango_IN_DTOWN, pefect..... K = 2 or k + -2

Answer 8

Thanks guys so for B) 3x^2 - x + k k = 2 or k = -2

Answer 9

and for A) 1 and -15 ?

Answer 10

could you help explain please

Answer 11

for number 1)
your coefficient of x^2 is just 1...
so all you need to do is look at what two numbers multiply to be -15
and then just add those numbers to find k.
you should get 4 answers here.
for number 2)
your coefficient of x^2 is something other than 1...
so you need to find what two factors of a*c have product a*c and sum b.
for number 2 let's say the product of 3k is m*n such that m+n=b where b=-1 in this case
so we have 3k=mn and m+n=-1
solve m+n=-1 for either m or n.
I choose to solve for m giving me m=-n-1 or m=-(n+1)
plugging this into 3k=mn we get 3k=-n(n+1)
This means 3k needs to be chosen to be negative product of 2 consecutive integers
so 3k=-n(n+1) means 3 could be -n and k could be n+1
or 3k=-n(n+1) means 3 could be n and k could be -(n+1)
or 3k=-n(n+1) means 3 could be n+1 and k could be -n
or 3k=-n(n+1) means 3 could be -(n+1) and k could be n
so of the 4 cases here...playing with these you will only see there actually only 2 possible answers for B

Answer 12

so summary
you should have 4 answers for A
and 2 answers for B