Question

solve:
. $6q^{2} - 17q + 12$
. $8s^{2} + 2s - 15$

Answer 1

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 ;

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

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

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

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

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

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

${:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}$

Now, turning to the second equation ;

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

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

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

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

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

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

${:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}$

Answer 2

Answer:

Below in bold.

Step-by-step 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.