Question

Suppose you were given the function F(x) = x^4 − 2x^3 + 3x^2 − ax + 3 and the factor (x − 2). What is the value of a?

Answer 1

ANSWER

$a=7.5$

EXPLANATION

We want to find the value of a for the given function and its factor.

Since (x - 2) is a factor of the function, it means that if 2 is substituted for x in the function, it will equate to 0.

This implies that:

$\begin{gathered} F(2)=(2)^4-2(2)^3+3(2)^2-a(2)+3=0 \\ 16-16+12-2a+3=0 \\ 15-2a=0 \end{gathered}$

Solve the equation for a:

$\begin{gathered} 2a=15 \\ a=\frac{15}{2} \\ a=7.5 \end{gathered}$

That is the value of a.