Determine where the real zeros of f(x)= 2x^4 + x^2 - 3x + 3 are locateda.between -1 & 0c.between 1 & 2b.between 0 & 1d.no real zeros
Accepted Solution
A:
The given polynomial is f(x) = 2x⁴ + x² - 3x + 3 There are 2 changes of sign
From Descartes' Rule of signs, there are (a) 2 real positive zeros, or (b) a conjugate pair of 2 complex zeros.
f(-x) = 2x⁴ + x² + 3x + 3 There is no change in sign There are no negative real zeros.
Let us test for real zeros in the given ranges: x f(x) ----- -------- -1 9 -0.5 4.875 0 3 0.5 1.875 1 3 1.5 10.875 2 33 There are no changes in the sign of f(x). Therefore no real zeros exist in (-1,0), (1,2), (0,1). The graph of the function confirms the conclusion.