Solve by completing the square. 4x^2 + 8x– 3=0

x = -1 + , x = -1 -

Step-by-step explanation:

4 + 8x - 3 = 0

First, add 3 to both sides:

4 + 8x = 3

Next, divide both sides by 4:

+ 2x =

Now, add the correct number by dividing 2 by 2 and squaring it and add it to both sides:

+ 2x + 1 =

Then, factor the left side:

=

Next, take the square root of both sides:

x + 1 = ±

Solve for x:

x = -1 + , x = -1 -

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.