Consider eqn of the form x^2 + bx + c = 0. The number of such ...?

equations that have real roots and have coefficients b and c in the set {1,2,3,4,5,6}, (b may be equals to c), is


A) 20;


B) 18;


C) 17;


D) 19;


Please explain, Thanks...

Consider eqn of the form x^2 + bx + c = 0. The number of such ...?
6 ways to choose b


6 ways to choose c


36 possible ways to choose b and c (note that not all of them will have real roots)





For the equation to have real roots: b²≥4c


For b=1: no real roots


For b=2: c = 1


For b=3: c = {1, 2}


For b=4: c = {1, 2, 3, 4}


For b=5: c = {1, 2, 3, 4, 5, 6}


For b=6: c = {1, 2, 3, 4, 5, 6}





Number of possible equations = 1×0 + 1×1 + 1×2 + 1×4 + 1×6 + 1×6 = 19





D
Reply:Real roots if Delta%26gt;=0


ie b^2 -4c %26gt;=0


b^2 %26gt;=4c





List the possibilities


b=1


no values of c





b=2, c=1


b=3, c=1,2,


b=4, c=1,2,3,4


b=5, c=1,2,3,4,5,6


b=6, c=1,2,3,4,5,6





So 19 possibilities


c=1

forsythia