x^2+7[x]+5=0 what is the sum of the roots of the equation?

Question

here [x] denotes the greatest integer less than or equal to x

Answer 1

we have a polynomial equation of degree 2 , which implies we have 2 solutions. As a quadratic function, we can solve the equation by factoring method or using the quadratic formula such as x = (-b +- √b² -4ac)/2a

The standard form of a quadratic equation is aX²+bx+c=0 . 

IN our case a=1 , b=7 c =5. 

SInce we cannot find two numbers where the product is 5 and the sum is 7, this denotes that our solutions are not integer, therefore we need to use the quadratic formula mentioned above. 

so .. x = (-7+-√(7)^2 -4*1*5)/2   = (-7 +- √49-20)/2 = (-7 +- √29)/2 

one solution is (-7+√29)/2 and the other one is (-7-√29)/2 

the sum of the solution =  (-7 + √29)/2 +  (-7 + √29)/2 = -7 

a short answer to find the sum of the solution is using -b/a and the product =c/a