math
posted by hiroko .
Find all rational zeros of the function. Then (if necessary) use the depressed equation to find all roots of the equation f(x)=0
f(x)= 5x^411x^333x^2+77x14

trying x = ±1, ±2, ± 7, ±1/5, ±2/5, ±7/5
I found f(2) = 0
and f(x) = (x2)(5x^3  x^2  35x + 7) = (x2)g(x)
x = ±7 didn't work in the first, so it certainly will not work in this one
so try x = 1/5 in the cubic factor
g(1/5) = 5(1/125)  1/25  35(1/5) + 7 = 0
so we have
f(x) = (x2)(5x1)(x^2  7) after a division
roots are
x = 2, 1/5, ± √7