Question

Can somebody plz help me

Answer 1

Answer: A

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=
  `(-2-√(76) )/(4)` (-b+√76)/4=
  `(-2+√(76) )/(4)`

the trick here is to notice that :

`√(76)` =
`√(19*4)`

=
`√(19) *√(4)`

= 2
`√(19)`

Now we will simplify Δ by factoring by 2

• 
  `(2*(-1(+/-)√(19) )/(2*2)` =
  `(-1(+/-)√(19) )/(2)`

so the answer is a .