If f(x)=x^5+x^4-5x^3-2x^2+6x-2,g(x)=x^5-3x^3+2x^2-4x+2. How many distinct numbers ‘a’ satisfy f(a)=g(a)=0? a) 1 b)2 c)3 d)4 e)0

Answer 1

e) 0

g(x) has 3 negative zeros about -2.4, -1.2 and -0.3

f(x) has 2 positive zeros about .5 and 1.6, and 1 negative zero about -2.2

both have two imaginary zeros

but there is no a such that f(a) = g(a) = 0

if you rounded to nearest integer then -2.2 and -2.4 become both -2.2 = a

and that's one a such that f(a) = approximately g(a)

graph f and g and you see f and g each intersect the x axis 3 time but never at the same point

altho -2.2 and -2.4 is fairly close