Question

If a and b are the zeros of polynomial x2-4x+1, find the value of a+1/a .

Answer 1

Answer:

The answer is 4

Step-by-step explanation:

Since $a$ is a zero of $x^2-4x+1$

$\Rightarrow a^2-4a+1=0\\\Rightarrow a^2+1=4a$

Divide both sides by $a$

$\Rightarrow \frac{a^2+1}{a}=\frac{4a}{a}\\\Rightarrow \frac{a^2}{a}+\frac{1}{a}=4\\\therefore a+\frac{1}{a}=4$