Answer:
Roots are -3, 1 and 2 ( * 2).
The y intercept is y = -12.
Step-by-step explanation:
Roots of =:
x^4 - 2x^3 - 7x^2 + 20x - 12 = 0
Try x = 1:
Left side = 1^4 - 2*1^3 - 7 * 1^2 + 2*1 - 12
= 1 - 2 - 7 + 20 -12
= -8 + 20 -12
= 12 - 12
= 0.
So one root is x = 1.
Try x = -1:
this works ot to -57 so x = -1 is not a root.
Try x = 2:
This works ot to 0
So x = 2 is a root.
Now we know that (x - 1)(x - 2) (= x^2 - 3x + 2) is a factor of f(x) so dividing:
x^2 - 3x + 2)x^4 - 2x^3 - 7x^2 + 20x - 12(x^2 + x - 6 <---Qotient
x^4 - 3x^3 + 2x^2
x^3 - 9x^2 + 20x
x^3 - 3x^2 + 2x
-6x^2 + 18x - 12
-6x^2 + 18x - 12
Now x^2 + x - 6 = (x + 3)(x - 2)
The last 2 roots are therefore:
x = 2 and x = -3.
y-intercept
Here the x vale is 0
so it is 0 + 0 + 0 + 0 -12
= -12.
