Use Descartes rule of signs to determine the different possi

Use Descartes\' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros for the following function. f(x) = -4x^4 + 7x^3 - 9x^2 + 7x - 17 The possible number of positive real zeros is (Type a whole number. Use a comma to separate answers as needed.)

Solution

given f(x)=-4x⁴+7x³-9x²+7x-17

sign of coefficients changes 4 times from left to right

the possible number of positive real zeroes is 4,2,0

f(-x)=-4x⁴-7x³-9x²-7x-17

sign of coefficients changes 0 times from left to right

the possible number of negative real zeroes is 0

the possible number of nonreal complex zeroes is 4,2,0