Solving quadratics

the value of danielle's investments is modeled by the equation v (t)=3t^2+70t+100
where t represents the number of months after she made her initial investment. jeffrey has no money invested in stocks, but he deposits the same amount every month into a savings account that he opened at the same time as danielle. his savings account balance can be modeled by the equation v (t)=50t+275

after how many months will the value of danielle's investment be equal to jeffery's savings account?

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.

52.5

step-by-step explanation: