Question

Solve:
.
`6q^(2) - 17q + 12`
.
`8s^(2) + 2s - 15`

Answer 1

Below in bold.

Explanation:

I am assuming you want to factor these expressions.

6q^2 - 17q + 12

We need 2 numbers whose product is (6*12) = 72 and whose sum is -17.

Theses are -9 and -8 so we write:

= 6q^2 - 9q - 8q + 12

= 3q(2q - 3) - 4(2q - 3)

= (3q - 4)(2q - 3)

If you want the solution of this expression = zero they are q = 4/3, 3/2.

8s^2 + 2s - 15

8 * -15 = -120. -120 = -2 * 2 * 2 * 3 * 5 = +12 * -10 ( to give the +2s)

= 8s^2 + 12s - 10s - 15

= 4s(2s + 3) - 5(2s + 3)

= (4s - 5)(2s + 3)

If you want the solution of this expression = zero they are s = 5/4, -3/2.

Answer 2

For zeroes i.e for value(s) of q and s, the given equations must be equal to 0, so let's start with first equation and then 2nd equation ;

`{:\implies \quad \sf 6q^(2)-17q+12=0}`

`{:\implies \quad \sf 6q^(2)-9q-8q+12=0}`

`{:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}`

`{:\implies \quad \sf (3q-4)(2q-3)=0}`

`{:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}`

`{:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}`

`{:\implies \quad \bf q=(3)/(2),\frac43}`

Now, turning to the second equation ;

`{:\implies \quad \sf 8s^(2)+2s-15=0}`

`{:\implies \quad \sf 8s^(2)+12s-10s-15=0}`

`{:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}`

`{:\implies \quad \sf (4s-5)(2s+3)=0}`

`{:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}`

`{:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}`

`{:\implies \quad \bf s=(5)/(4),-\frac32}`