Ineed to solve the absolute value for |4q+9|=|2q-1| !

Step-by-step explanation:

If this has at least one solution then it will come from either 4q+9=2q-1 or from 4q+9=-(2q-1).

Let' solve the first:

4q+9=2q-1

Subtract 2q on both sides:

2q+9=-1

Subtract 9 on both sides:

2q=-10

Divide both sides by 2:

q=-5

Let's check it into the original equation:

|4(-5)+9|=|2(-5)-1|

|-20+9|=|-10-1|

|-11|=|-11|

11=11

So q=-5 checks out as a solution.

Let's solve the other equation:

4q+9=-(2q-1)

Distribute:

4q+9=-2q+1

Add 2q on both sides:

6q+9=1

Subtract 9 on both sides:

6q=-8

Divide both sides by 6:

q=-8/6

Reduce:

q=-4/3

Let's check it into the original equation:

|4(-4/3)+9|=|2(-4/3)-1|

|-16/3+9|=|-8/3-1|

|11/3|=|-11/3|

11/3=11/3

So q=-4/3 also checks out since both sides are the same when plugging in q=-4/3.

the answer is d

step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.