Answer

Verified

413.4k+ views

**Hint:**Above question is based on quadratic equations. So first we will learn some basics about them.

Quadratic equations- These are the Polynomial equations of degree 2 in one variable.

The quadratic equation will always have two roots. The nature of roots may be real or imaginary.

Lets understand them with and example-:

x² + 5x + 6 = 0

There are two roots of this equation. i.e. -2 and -3

When we place \[x = - 2\] or \[x = - 3\]

In the above equation they will satisfy it.

So, roots of equation- Real number will be called a solution or a root if it satisfies the equation.

I.e. a will be the root of equation,

If \[f\left( a \right) = 0\]

The solution or roots of a quadratic equation are given by the quadratic formula:

**Complete step by step solution:**Let number of dipole staying overnight $ = $ x

For x people the bill will be $ = $ Rs. 48000/.

So, for 1 person bill will be $ = Rs\left( {\dfrac{{4800}}{x}} \right)$

According to the question :

When 4 persons will more, bill will be $ = Rs\left( {\dfrac{{4800}}{{x + 4}}} \right)$

After adding 4 persons, bill paid by each person will reached by 200/-

Therefore

$\left( {\dfrac{{4800}}{x}} \right) - \left( {\dfrac{{4800}}{{x + 4}}} \right) = 200$

$4800(x + 4) - 4800x = x(x + 4) \times 200$

$4800x + 19200 - 4800x = ({x^2} + 4x)200$

$19200 = ({x^2} + 4x) \times 200$

$96 = {x^2} + 4x$ or ${x^2} + 4x - 96 = 0$

Which is a quadratic equation

So, we will calculate the roots of this equation by quadratic equation.

We know that $x = \dfrac{{ - B \pm \sqrt {{B^2} - 4AC} }}{{2A}}$

Where A $ = $ coefficient of ${x^2} = 1$

B $ = $ coefficient of $x = 4$

C $ = $ coefficient of $ = - 96$

Therefore,

$x = \dfrac{{ - 4 \pm \sqrt {{{(4)}^2} - 4(1)( - 96)} }}{{2 \times 1}}$

$x = \dfrac{{ - 4 \pm \sqrt {16 + 384} }}{2}$

$x = \dfrac{{ - 4 \pm \sqrt {400} }}{2}$

$x = \dfrac{{ - 4 \pm 20}}{2}$

$x = \dfrac{{ - 4 + 20}}{2}$ or $x = \dfrac{{ - 4 - 20}}{2}$

$x = 8$ or $x = - 12$

Since x denotes number of people,

So it can't be negative.

Therefore we will neglect the negative digit.

Hence,

The number of people staying over night \[ = x = 8.\]

Therefore option B i.e. 8 is the correct option.

**Note:**1. The roots of the quadratic equation:

\[x = \left( { - b \pm \surd D} \right)/2a\]

where,

; and called discriminant of equation.

We can determine the nature of roots by using this Discriminant.

(¡) \[D > 0,\] roots are real and distinct (unequal)

(¡¡)\[D = 0,\] roots are real and equal

(¡¡¡) \[D < 0,\] roots are imaginary and unequal

Recently Updated Pages

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

How do you find the general solution to dfracdydx class 12 maths CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE