Question

Use this fact to find all zeros of the function

Answer 1

Solution

Since the function has at least one rational zero, we can apply fthe actor theorem

The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0.

since f(1) = 0, f(-2) = 0

=> (x + 2) is a factor of f(x)

=> X - 1 IS also a factor

$(x+2)(x-1)=x^2-x+2x-2=x^2+x-2$

Solving

$x=\frac{1}{6}(1-\sqrt{13}),\frac{1}{6}(1+\sqrt{13}),-2,1$