A polynomial has been factored below, but some constants are missing.

From the information in the problem, the value of a is 2, the value of b is 2, and the value of c is -6.

Step-by-step explanation:

The first thing we have to do is factor the equation in order to find the value of a, b, and c.

2x³ - 8x² - 24x

Find a common factor that can be easily divisible among all the terms. This common factor is 2x. Factor the equation.

2x(x² - 4x - 12)

Now, we have to factor out the equation in the parentheses. we do this by multiplying the first term by the last term first. Since there is no coefficient number for x², then we assume this number to be 1.

1 × -12 = -12

Now, we have to find two numbers that multiply to get -12 but add together to get -4. These numbers are 2 and -6. Let's plug these numbers into the equation.

2x(x² + 2x - 6x - 12)

Group the first and second terms together and group together the third and last term together in the parentheses.

2x((x² + 2x) + (-6x - 12))

Factor the equation in parentheses.

2x(x + 2)(x - 6)

So, the value of a is 2, the value of b is 2, and the value of c is -6.

6 on both sides and twelve on the top and the bottom

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.