Question

Answer the following problems.

2.) Determine the sum pf the real zeros of P(x) = 3x⁴ + 14x³ + 10x² - 14x + 3.

3.) Find μ so that x - 3 is a factor of μx³ - 13x² - μx - 3.

Answer 1

2) The sum of the real zeros of P(x) is

$$-\frac{b}{a}=-\frac{14}{3}$$

3) By the Factor Theorem, x-3 is a factor of 

$$f(x)=μx^3 - 13x^2 - μx - 3\\f(3)=3^3μ - 13(3)^2 -3 μ - 3=0\\\mu=5$$