Px x5 3x3 x 2 no real zero less than 3Solution95 graph

P(x) = x^5 - 3x^3 + x + 2; no real zero less than -3

Solution

95 ) graph cuts the x axis at x= -5

zero at x=-5

graph touches the x axis at x = 3

zero at x=3 of multiplicity 2

Polynomial: f(x) = k(x+5)(x -3)^2

We would the constant k by using point (0, 9)

9 = k(5)(-3)^2

k= 1/5

f(x) = (1/5)(x+5)(x -3)^2   Polynomial