determine ** ALL** integral values of

1) x^2 + kx - 9

2) 3x^2 + kx + 7

determine __ TWO__ integral values of

1) x^2 - 3x + k

2) 3x^2 + 4x + k

Guest Jul 21, 2017

#1**+1 **

1) x^2 + kx - 9

The integers we are looking for here multiply to -9

These are -9 and 1 , -1 and 9 , -3 and 3

And k will sum to these, i,e. , k = -8, k = 8 and k =0

however, if k = 0, we won't have a trinomial..!!

2) 3x^2 + kx + 7

The integers that we are looking for here can be found thusly

(3x + 1) ( x + 7) → 3x^2 + 22x + 7 → k = 22

(3x + 7) ( x + 1) → 3x^2 + 10x + 7 → k = 10

1) x^2 - 3x + k

Consider that we have

(x + m) (x + n) = x^2 + (m + n)x + mn

So (m + n) = -3 and k = mn

Two integers that work are -7and 4...and their product will be k = -28

And another possibility is -9 and 6.......and their product is k = - 54

2) 3x^2 + 4x + k

To find a suitable pair, consider

(3x + m) ( x + n) = 3x^2 + (m + 3n) x + mn

So....m + 3n will add to 4 and k will be their product

This works if m = n = 1 and their product is k = 1

Another possibility is if m = `10 and = -2 and their product = k = -20

CPhill
Jul 21, 2017