HirePro Equations Quiz-1

Given expression = (x-7)(x-14)(x-21)..... and so on till (x-84)
The highest power in the expression is x^{12} and its coefficient is 1.
Therefore,x^{11} will give the negative value of sum of all the possible roots of the equation.
Coefficient of x^{11} = -(7+14+21+........+84) = -(7*78) = -546..

I. 8x^{2} – 23x + 15 = 0

8x^{2} – 8x – 15x + 15 = 0

8x (x – 1) – 15 (x – 1) = 0

(8x – 15) (x – 1) = 0

x = \frac{15}{8},1

II. 3y^{2} + 11y + 8 = 0

3y^{2} + 3y + 8y + 8 = 0

3y (y + 1) + 8 (y + 1) = 0

(3y + 8) (y + 1) = 0

y = -\frac{8}{3},-1

Hence, x > y

I. 2x^{2} – 23x + 56 = 0
2x^{2} – 16x – 7x + 56 = 0
2x (x – 8) – 7 (x – 8) = 0
(2x – 7) (x – 8) = 0
x = \frac{7}{2},8

II. 4y^{2} – 19y + 12 = 0
4y^{2} – 16y – 3y + 12 = 0
4y (y – 4) – 3 (y – 4) = 0
(4y – 3) (y – 4) = 0
y=x = \frac{3}{4},4

Hence, no relationship can be established.

Price of unit Ranveer Singh for Packet A = {10}{100} = \frac{1}{10} = 0.1
Price of unit Ranveer Singh for Packet B = {6}{50} = 0.12

Packet A is cheaper

(a+b)+(b+c)+(c+a) = 3 + 4 + 5
=> 2a + 2b +2c = 12
a + b + c = 6

To find the Y - intercept put x= 0
4*0 + y =12
y=12

x^{2} + 4 =104
x^{2} =104 - 4
x^{2} =100
x = 10

y=\frac{6-10x}{8x+7}

x=\frac{6-10y}{8y+7}

x(8y+7)=6−10y

8xy+7x=6−10y

8xy+10y=6−7x

(8x+10)y=6−7x

y=\frac{6-7x}{8x+10}

So,f(x)^{-1}=\frac{6-7x}{8x+10}

Number of persons * days = work
50 * 9 = 450 (work)
Now, x * 15 = 450 (work)
=> x =30
Therefore in the second case the required number of people
.

One day work of aman=1/30
One day work of Bharat=1/20
Both can complete work in =1/30+1/20
=5/60
Number of days = 60/5 = 12 days
Now we have to find the share of bharat So,
12 X \frac{1}{20} X 30000]
=18000