Question

3q^2+8q+5=0?

3q^2+8q+5=0

Answer 1

`q = -5/3`, `q = -1`

Explanation:

`3q^2+8q+5 = 0`

this can be factorised by grouping.

firstly, take the product of the first and third coefficients:

`3 * 5 = 15`

then find two numbers that add to the second coefficient and multiply to make the third one:

`3 + 5 = 8`
`3 * 5 = 15`

substitute the second coefficient for these numbers:

`3q^2 + (3+5)q + 5`

`3q^2 + 3q + 5q + 5`

then find the common factors between the first two and last two terms.

`3q^2 + 3q = 3q(q+1)`

`5q + 5 = 5(q+1)`

these terms now have a common factor, so they can be grouped together:

`3q(q+1) + 5(q+1) = (3q+5) (q+1)`

this will help to solve for `q`.

we are given that `3q^2+8q+5 = 0`.

we therefore know that `(3q+5) (q+1) = 0`.

`0` can only be the product of two numbers if at least one is `0`.

`3q+5` and `q+1` are different expressions, so there are two possible values that `q` can have, so that either is `0`.

either `3q + 5 = 0` or `q + 1 = 0`.

if `3q + 5 = 0`, then `3q = -5` and `q = -5/3`.

if `q + 1 = 0`, then `q = -1`.

the two solutions for `q` are `-5/3` and `-1`.