Question

Step by step instructions

Answer 1

If our two roots are
`r` and
`s` we can write

`0 = (x-r)(x-s) = x^2 + bx + 6`

`x^2 -(r+s)x+rs = x^2 + bx + 6`

Matching coefficients,

`-(r+s) = b`

`rs = 6`

"Positve integral" is a fancy way of saying natural number, 1, 2, 3, ...

So these are the factors pairs of six:

`6=1 \cdot 6 = 2 \cdot 3`

The two possible sums are 1+6=7 and 2+3=5. b is the negative sum.

Answer: b=-7 or b=-5