Question

Select the correct answer from each drop-down menu.

m^2-5/2m=-11/2 , m=___±___.

1st options:
1/4
1
5/4

2nd options:
(3i square root 7)/4
(i square root 21)/2
(square root 113)/4

Answer 1

correct option for first blank is 5/4 and for second blank is
`( 3i√(7))/(4)`

i.e m=
`(5)/(4)\pm( 3i√(7))/(4)`

Explanation:

The given equation

`m^2 - \frac {5m}{2} = (-11)/(2)`

and we have to find m= ______ ± ________

We can use quadratic formula to solve this question.

The above equation can be written as:
`m^2 - \frac {5m}{2} + (11)/(2) = 0`

and the formula used will be:

`m= (-b\pm√(b^2-4ac))/(2a)`

Putting values of a= 1, b= -5/2 and c= 11/2 and solving we get:
`m=\frac{-(-5)/(2)\pm\sqrt{{((-5)/(2))}^2-4(1)((11)/(2))}}{2(1)}\\\\m=\frac{(5)/(2)\pm\sqrt{((25)/(4))-22}}{2}\\m=\frac{(5)/(2)\pm\sqrt{((-63)/(4))}}{2}\\m= ((5)/(2))/(2)\pm\frac{\sqrt{((-63)/(4))}}{2}\\m= (5)/(4)\pm(√(-63))/(4)`

Since there is - sign inside the √ so
`√(-1)` is equal to i and we have to divide
`√(63)` into its multiples such that the square root of one multiple is whole no so,

`√(63)` =
`√(9)* √(7)`=
`3* √(7)`

Putting value of
`√(63)` and
`√(-1)`

the value of m=
`(5)/(4)\pm( 3i√(7))/(4)`

so, correct option for first blank is 5/4 and for second blank is
`( 3i√(7))/(4)` .