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Sagot :
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 ;
[tex]{:\implies \quad \sf 6q^{2}-17q+12=0}[/tex]
[tex]{:\implies \quad \sf 6q^{2}-9q-8q+12=0}[/tex]
[tex]{:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}[/tex]
[tex]{:\implies \quad \sf (3q-4)(2q-3)=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}[/tex]
[tex]{:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}[/tex]
Now, turning to the second equation ;
[tex]{:\implies \quad \sf 8s^{2}+2s-15=0}[/tex]
[tex]{:\implies \quad \sf 8s^{2}+12s-10s-15=0}[/tex]
[tex]{:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}[/tex]
[tex]{:\implies \quad \sf (4s-5)(2s+3)=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}[/tex]
[tex]{:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}[/tex]
[tex]{:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}[/tex]
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.
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