Question

The choices for the first one is

1/4

1

5/4

Choice for the second one is
(3i square root 7)/4

(i square root 21)/2

(square root 112)/4

Answer 1

`\large\boxed{(5\pm3\sqrt7)/(4)}`

Explanation:

`m^2-(5)/(2)m=-(11)/(2)\qquad\text{add}\ (11)/(2)\ \text{to both sides}\\\\m^2-(5)/(2)m+(11)/(2)=0\qquad\text{multiply both sides by 2}\\\\2m^2-5m+11=0`

`\text{Use the quadratic formula:}`

`ax^2+bx+c=0\\\\x=(-b\pm√(b^2-4ac))/(2a)`

`\text{We have}`

`a=2,\ b=-5,\ c=11`

`\text{substitute:}`

`√(b^2-4ac)=√((-5)^2-4(2)(11))=√(25-88)=√(63)=√(9\cdot7)=\sqrt9\cdot\sqrt7=3\sqrt7\\\\m=(-(-5)\pm3\sqrt7)/(2(2))=(5\pm3\sqrt7)/(4)`