Question

Can somebody plz help me

Answer 1

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

• b= -2
• a=  2
• c=  -9

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= $\frac{-2-\sqrt{76} }{4}$         (-b+√76)/4=$\frac{-2+\sqrt{76} }{4}$  

the trick here is to notice that :

$\sqrt{76}$ = $\sqrt{19*4}$

      = $\sqrt{19} *\sqrt{4}$

      = 2$\sqrt{19}$

Now we will simplify Δ by factoring by 2

• $\frac{2*(-1(+/-)\sqrt{19} }{2*2}$ = $\frac{-1(+/-)\sqrt{19} }{2}$

so the answer is a .