Answer: A
Step-by-step explanation:
2x²-2x-9=0
this is a quadratic equation so we will use the quadratic formula .
Δ= b²-4*a*c
let's calculate Δ to khow how many solutions this equations have .
Δ= (-2)²-4*2*(-9)
= 76
we notice that 76>0
so this equation has two solutions : (-b-√76)/4 and (-b+√76)/4
- let's calculte the values :
- (-b-√76)/4= [tex]\frac{-2-\sqrt{76} }{4}[/tex] (-b+√76)/4=[tex]\frac{-2+\sqrt{76} }{4}[/tex]
the trick here is to notice that :
[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]
= [tex]\sqrt{19} *\sqrt{4}[/tex]
= 2[tex]\sqrt{19}[/tex]
Now we will simplify Δ by factoring by 2
- [tex]\frac{2*(-1(+/-)\sqrt{19} }{2*2}[/tex] = [tex]\frac{-1(+/-)\sqrt{19} }{2}[/tex]
so the answer is a .
