Question

State the possible number of positive real zeros, negative realzeros, and imaginary zeros for each function.

13.f(x) = ­-x^3 -­ x2 + 14x -­ 24

14.f(x) = 2x^3 -­ x^2 + 16x -­ 5

Answer 1

In general, y = ax³ + bx² + cx + d

Where a,b,c & d are real,

Y can have at max 3 real roots, or one real and a conjugate pair of complex roots.

Also, -d/a is the product of roots

13) positive real values: 0 or 2

negative real values: 1 or 3

Imaginary roots: 0 or 2

14) positive real values: 1 or 3

negative real values: 0 or 2

Imaginary roots: 0 or 2