Question

The expression x4 + 6x3 – 11x2 – 60x + 100 is equivalent to (x – 2)(x – 2)(x + 5)(x + 5). At what points does the graph of the function f(x) = x4 + 6x3 – 11x2 – 60x + 100 intersect the x-axis?

Answer 1

Answer:

(2,0) and (-5,0)

Step-by-step explanation:

Since, if (x-a) is the factor of a polynomial then the graph of the polynomial intersects the x-axis at (a,0).

Here, the given polynomial,

$x^4+6x^3-11x^2-60x+100$

According to the question,

$x^4+6x^3-11x^2-60x+100=(x-2)(x-2)(x+5)(x+5)$

⇒ (x-2) and (x+5) are the factors of the given polynomial,

By the above statement,

The points at which the graph of the given function intersects the x-axis are,

(2,0) and (-5,0)

Answer 2

Since y equals the product of the factors, any value for x which makes any factor equal to zero is a point where the graph touches the x-axis.

x=-5 and 2  (technically the points (-5,0) and (2,0))