Find the Y-intercepts & X-intercepts of F(X)

Question

F(x)=X³-7x²+14x-6

Answer 1

Hello Khalif,

 

We find the y intercept by setting x=0 and solving for F(x) which is y

 

F(0) = 0³-7(0²)+14(0)-6 = -6

The y intercept is at the point (0,-6)

 

The x intercepts are determined when y = 0

0 = x³-7x²+14x-6

To solve, we need to factor

(x-3)(x²-4x+2)

 

We can set x-3=0 and solve for x

x = 3

 

for the other factor, we need to use the quadratic formula to solve for x

 

-b±√(b²-4ac)

---------------

       2a

And we get 2±√2

 

So our 3 x-intercepts are 3, 2+√2 and 2-√2